539 lines
6.9 KiB
Plaintext
539 lines
6.9 KiB
Plaintext
ans
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021268
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\begin{center}
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\begin{tabular}{|c|c|c|c|c|c|}
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\hline 标准方程 & 图形 & 顶点 & 对称轴 & 焦点 & 准线 \\
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\hline $y^2=2 p x$($p>0$) & \begin{tikzpicture}[>=latex,scale = 0.5]
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\draw [->] (-2,0) -- (2,0) node [below] {$x$};
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\draw [->] (0,-2) -- (0,2) node [right] {$y$};
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\draw (0,0) node [below right] {$O$};
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\draw (-0.5,-2) -- (-0.5,2);
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\draw [domain = -2:2] plot ({\x*\x/2},\x);
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\end{tikzpicture} & $(0,0)$ & $x$轴 & $(\frac{p}{2},0)$ & $x=-\frac{p}{2}$ \\
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\hline $y^2=-2 p x$($p>0$)& \begin{tikzpicture}[>=latex,scale = 0.5]
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\draw [->] (-2,0) -- (2,0) node [below] {$x$};
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\draw [->] (0,-2) -- (0,2) node [right] {$y$};
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\draw (0,0) node [below right] {$O$};
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\draw (0.5,-2) -- (0.5,2);
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\draw [domain = -2:2] plot ({-\x*\x/2},\x);
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\end{tikzpicture} & $(0,0)$ & $x$轴 & $(-\frac{p}{2},0)$ & $x=\frac{p}{2}$ \\
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\hline $x^2=2 p y$($p>0$)& \begin{tikzpicture}[>=latex,scale = 0.5]
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\draw [->] (-2,0) -- (2,0) node [below] {$x$};
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\draw [->] (0,-2) -- (0,2) node [right] {$y$};
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\draw (0,0) node [below right] {$O$};
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\draw (-2,-0.5) -- (2,-0.5);
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\draw [domain = -2:2] plot (\x,{\x*\x/2});
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\end{tikzpicture}& $(0,0)$ & $y$轴 & $(0,\frac{p}{2})$ & $y=-\frac{p}{2}$ \\
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\hline $x^2=-2 p y$($p>0$)&\begin{tikzpicture}[>=latex,scale = 0.5]
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\draw [->] (-2,0) -- (2,0) node [below] {$x$};
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\draw [->] (0,-2) -- (0,2) node [right] {$y$};
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\draw (0,0) node [below right] {$O$};
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\draw (-2,0.5) -- (2,0.5);
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\draw [domain = -2:2] plot (\x,-{\x*\x/2});
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\end{tikzpicture} & $(0,0)$ & $y$轴 & $(0,-\frac{p}{2})$ & $y=\frac{p}{2}$ \\
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\hline
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\end{tabular}
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\end{center}
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021270
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$(0,-8)$; $y=8$
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021271
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$(0,\frac{1}{16})$; $y=-\frac{1}{16}$
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021272
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$(0,-\frac{1}{6})$; $y=\frac{1}{6}$
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041007
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(1) $y^2=-x$; (2) $y^2=4x$或$y^2=-4x$或$x^2=-4y$或$x^2=4y$; (3) $y^2=-\frac{16}{3}x$或 $x^2=\frac{9}{4}y$;
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(4) $y^2=16x$或$y^2=-16x$;
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(5) $y^2=16x$或$x^2=-12y$.
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021276
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$\frac{5}{2}$
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021279
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$(3,\pm 2\sqrt{3})$
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021284
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$(3,\pm 2\sqrt{6})$
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021269
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A
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021275
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$(\frac{m}{4},0)$;$x=-\frac{m}{4}$
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041008
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$(0,\frac{1}{4a})$;$y=-\frac{1}{4a}$
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041009
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$y^2=12x$
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041010
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2
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041011
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$y^2=-8x$;$m=\pm 2\sqrt{6}$
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008929
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$x^2=-y,x\in [-1,1]$
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041012
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(1) $(-1,0)$;$x=1$; (2) $\frac{x^2}{2}+y^2$=1; (3) $(4-3\sqrt{2},\pm \sqrt{12\sqrt{2}-16})$
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021278
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$(1,\pm 2)$
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041013
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最小值为$4$, $M(\frac{1}{4},1)$
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041014
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$x^2=-12y$
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021280
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$y^2=x$
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041015
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$y^2=8x$
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021304
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$\frac{\pi}{2}$
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021308
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$\frac{11}{2}$
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021287
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$\frac{45}{8}$
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009840
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$(\frac{1}{4},0)$;$x=-\frac{1}{4}$
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021309
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2
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021290
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$(\frac{1}{2},1)$
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021291
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$y^2=2x$或$y^2=6x$
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041016
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相切
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021339
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$x^2-x+y^2=0(x\neq 0)$
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021289
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$4\sqrt{3}$
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021293
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3
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021294
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$(4,2)$
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021295
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$-4$
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021305
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$y^2=\pm 4x$
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013106
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$[-1,1]$
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021292
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B
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008930
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$0$或$-\frac{1}{2}$
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008934
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$4x-y-15=0$
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008922
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$y=\frac{1}{4},x>\frac{1}{16}$
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021299
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2
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021300
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$2\sqrt{15}$
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021321
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(1) 定点$(2,0)$;(2) 4
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041017
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(1) 6; (2) $\frac{1}{32}$
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041018
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8
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021316
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$\frac{11}{4}$
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021326
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8
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021319
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$y=\pm \frac{\sqrt{3}}{3}x+1$
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041019
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$\frac{2}{p}$
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041020
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D
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041021
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(1) $\frac{5p}{8}$; (2) $-2$;$-\frac{p}{y_0}$
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021331
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D
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041022
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C
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041023
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必要不充分
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021334
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$y=2x-3,x \leq 2$; $y=2x-3,x \in [1,2]$
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021335
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$y=-2x^2+8x-4$
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021336
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$y^2=8x-16$
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021337
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$x^2+y^2=1$
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021338
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$3x+y-4=0(x \neq 1)$
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021340
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$(x-1)^2+(y-2)^2=\frac{1}{9}$
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021341
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$x+2y-5=0$
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021342
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$x^2+y^2=4(x>0,y>0)$
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021343
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$(x-3)^2=10y-15$
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041024
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C
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008846
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0或$-\frac{1}{2}$
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008847
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$\frac{3}{2}$
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008852
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0或$\frac{1}{4}$或$-\frac{1}{2}$
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008853
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$[-4,4]]$
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041025
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(2) $13x-2y=0$
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041026
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$(-3,5),(1,1)$
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041027
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$k<-2$或$k>2$或$k=\pm \sqrt{3}$
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010704
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$(-\frac{2\sqrt{13}}{13},\frac{2\sqrt{13}}{13})$
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010703
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当$0<k<1$时,轨迹为椭圆;当$k>1$时,轨迹为双曲线;当$k=1$时,轨迹为抛物线
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021348
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$x^2+4(y-1)^2=4(0 \leq x \leq 2, 1 \leq y \leq 2)$
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021349
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0
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021351
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$\frac{\pi}{3}$或$\frac{2\pi}{3}$
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041028
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$(\frac{3\sqrt{3}}{2},1)$; $\arctan \frac{2\sqrt{3}}{9}$
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021352
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4
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021353
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D
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041029
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$x=a+r\cos \alpha, y=b+r \sin \alpha$ ($\alpha$为参数, $\alpha \in \mathbf{R}$)
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021354
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(1) $M_1$在曲线$C$上, $M_2$不在曲线$C$上; (2) $a=9$
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021355
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$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$双曲线
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009845
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$x=\frac{2+\cos \alpha}{2}, y=\frac{\sin \alpha}{2}$ ($\alpha$为参数, $\alpha \in \mathbf{R}$)
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009846
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$x=1+9t,y=1+12t$,其中 $t$ 为参数,$t\geq 0$
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021358
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6
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021359
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$\sqrt{17}$
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021362
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$(3\sqrt{2},\sqrt{2})$
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021363
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最大值7; 最小值$\frac{3\sqrt{15}-4}{4}$
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021364
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$\sqrt{33}+2\sqrt{6}$
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012470
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B
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041030
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B
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041031
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A
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041032
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$(-3,-\frac{3\sqrt{5}}{5}) \cup (\frac{3\sqrt{5}}{5},3)$
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041033
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13
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041034
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$\frac{1+2\sqrt{21}}{3}$
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041035
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$y=\pm 1$
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041036
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$y^2=2x-2$
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041037
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$7\sqrt{3}$
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041038
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(1) $C_1$是以$(-4,3)$为圆心,半径为1的圆; $C_2$是椭圆
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$\frac{x^2}{64}+\frac{y^2}{9}=1$; (2) $\frac{8\sqrt{5}}{5}$
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041039
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(1) $x=1$,$5x-2y-3=0$,$2x-y-1=0$,$2x+y-3=0$;
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(2) 点 $T$ 不在曲线 $\Gamma$ 上
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ans
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041073
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(-2,$\dfrac{1}{2}$)
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041074
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$x-8y=0(x<-\dfrac{8}{15}\sqrt{15}$或$x>\dfrac{8}{15}\sqrt{15}$)
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041075
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$(-\infty,-1)\cup(1,+\infty)$
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041076
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$[3+2\sqrt{3},+\infty)$
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041077
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$2\sqrt{10}$
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041078
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44
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002112
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$y^2=4x$
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002409
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$y^2=-\dfrac{9}{2}x$或$x^2=\dfrac{4}{3}y$
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041079
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$\pm 2\sqrt{6}$
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041080
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(5,0)
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041081
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$\dfrac{23}{24}$
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041082
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176.0
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041083
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$|PA|_{\min}=\begin{cases}
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a,0<a\leq1\\
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\sqrt{2a-1},a>1
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\end{cases}$
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041084
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不存在
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041085
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(1)$m_A=91.5,m_B=90\\(2)S^2_A<S^2_B,A$稳定\\(3)$\dfrac{4}{5}$
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041086
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(1)$1<a<\sqrt{10}\\(2)l:x=3$或$x=\pm \dfrac{5}{7}\sqrt{7}+3$
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041087
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(1)$d=2$\\(2)$P$不存在\\(3)$l:x=\pm \sqrt{2}y+2$
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002112
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$y^2=4x$
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002409
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$y^2=-\dfrac{9}{2}x$或$x^2=\dfrac{4}{3}y$
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041079
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$\pm 2\sqrt{6}$
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041080
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$(5,0)$
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041088
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$2x\pm \sqrt{3}y-2=0$
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003441
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$\dfrac{11}{4}$
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041089
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$2x+y-2=0$
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041090
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$(2,2)$
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041091
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1$\quad(\dfrac{1}{9},\dfrac{2}{3})$
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041092
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$48$
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041093
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C
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041094
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$S_{max}=30$此时$P(8,4)$
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041095
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(1)$x_B+x_C=11\\y_B+y_C=-4$\\(2)$BC:y=-4x+20$\\(3)$B(\dfrac{11-\sqrt{21}}{2},-2+2\sqrt{21})$\\C($\dfrac{11+\sqrt{21}}{2},-2-2\sqrt{21})$
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041096
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$(1)C_2:\dfrac{y^2}{4}-\dfrac{x^2}{3}=1\\(2)p>\dfrac{4}{3}\sqrt{3},\quad \overrightarrow{FA}\cdot \overrightarrow{FB}_{max}=9,\quad$此时$p=2\sqrt{3}$\\(3)$p=2\sqrt{3}$
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041097
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$(-\infty,-2)$
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041098
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$\dfrac{1}{2}$
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041099
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(2)(3)(4)
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018928
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7
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041100
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AD,CD
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041101
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(3)(4)
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041102
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$\pm 2$
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041103
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$y^2-\dfrac{x^2}{48}=1\quad(y<0)$
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041104
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4或2或$\dfrac{3}{2}$
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041105
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(2)
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023553
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(1)$\dfrac{17}{45}$\\(2)一级6箱，二级2箱\\(3)预估287.69克
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041106
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$[\dfrac{1}{3},1)\cup(1,3]$
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018949
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没有被抓的风险
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041107
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(1)$\dfrac{x^2}{24}+\dfrac{y^2}{20}=1\\S_{max}=\dfrac{5\sqrt{30}}{4}$
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041108
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D
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041109
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C
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041110
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A
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041111
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B
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041112
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$\dfrac{2}{5}\sqrt{10}$
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041113
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A
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030201
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B
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041114
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A
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041115
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$(\sqrt{3},2)$
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041116
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$\dfrac{\sqrt{2}}{2}$
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041117
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(1)$arccos\dfrac{2}{5}\\$(2)正弦值为$\dfrac{\sqrt{15}}{5}\\(3)\dfrac{\pi}{6}$
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041118
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$l:y-2=\dfrac{118}{143}(x-3)$
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041119
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$x^2+y^2+x-6y+3=0$
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041120
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曲线方程为$y^2=48-12x\quad(x\geq3)$及$y^2=4x\quad(x<3)$
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041121
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$x^2+y^2=7$
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ans
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012345
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D
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023233
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$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
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\end{cases}$.
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023255
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(1)略；(2)$a_n=\begin{cases}
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\frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2
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\end{cases}$
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