ans

021268
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline 标准方程 & 图形 & 顶点 & 对称轴 & 焦点 & 准线 \\
\hline $y^2=2 p x$($p>0$) & \begin{tikzpicture}[>=latex,scale = 0.5]
\draw [->] (-2,0) -- (2,0) node [below] {$x$};
\draw [->] (0,-2) -- (0,2) node [right] {$y$};
\draw (0,0) node [below right] {$O$};
\draw (-0.5,-2) -- (-0.5,2);
\draw [domain = -2:2] plot ({\x*\x/2},\x);
\end{tikzpicture} & $(0,0)$ & $x$轴 & $(\frac{p}{2},0)$ & $x=-\frac{p}{2}$ \\
\hline $y^2=-2 p x$($p>0$)& \begin{tikzpicture}[>=latex,scale = 0.5]
\draw [->] (-2,0) -- (2,0) node [below] {$x$};
\draw [->] (0,-2) -- (0,2) node [right] {$y$};
\draw (0,0) node [below right] {$O$};
\draw (0.5,-2) -- (0.5,2);
\draw [domain = -2:2] plot ({-\x*\x/2},\x);
\end{tikzpicture} & $(0,0)$ & $x$轴 & $(-\frac{p}{2},0)$ & $x=\frac{p}{2}$ \\
\hline $x^2=2 p y$($p>0$)& \begin{tikzpicture}[>=latex,scale = 0.5]
\draw [->] (-2,0) -- (2,0) node [below] {$x$};
\draw [->] (0,-2) -- (0,2) node [right] {$y$};
\draw (0,0) node [below right] {$O$};
\draw (-2,-0.5) -- (2,-0.5);
\draw [domain = -2:2] plot (\x,{\x*\x/2});
\end{tikzpicture}& $(0,0)$ & $y$轴 & $(0,\frac{p}{2})$ & $y=-\frac{p}{2}$ \\
\hline $x^2=-2 p y$($p>0$)&\begin{tikzpicture}[>=latex,scale = 0.5]
\draw [->] (-2,0) -- (2,0) node [below] {$x$};
\draw [->] (0,-2) -- (0,2) node [right] {$y$};
\draw (0,0) node [below right] {$O$};
\draw (-2,0.5) -- (2,0.5);
\draw [domain = -2:2] plot (\x,-{\x*\x/2});
\end{tikzpicture} & $(0,0)$ & $y$轴 & $(0,-\frac{p}{2})$ & $y=\frac{p}{2}$ \\
\hline
\end{tabular}
\end{center}

021270
$(0,-8)$; $y=8$

021271
$(0,\frac{1}{16})$; $y=-\frac{1}{16}$

021272
$(0,-\frac{1}{6})$; $y=\frac{1}{6}$

041007
(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 $x^2=\frac{9}{4}y$;
(4) $y^2=16x$或$y^2=-16x$;
(5) $y^2=16x$或$x^2=-12y$.

021276
$\frac{5}{2}$

021279
$(3,\pm 2\sqrt{3})$

021284
$(3,\pm 2\sqrt{6})$

021269
A

021275
$(\frac{m}{4},0)$;$x=-\frac{m}{4}$

041008
$(0,\frac{1}{4a})$;$y=-\frac{1}{4a}$

041009
$y^2=12x$

041010
2

041011
$y^2=-8x$;$m=\pm 2\sqrt{6}$

008929
$x^2=-y,x\in [-1,1]$

041012
(1) $(-1,0)$;$x=1$; (2) $\frac{x^2}{2}+y^2$=1; (3) $(4-3\sqrt{2},\pm \sqrt{12\sqrt{2}-16})$

021278
$(1,\pm 2)$

041013
最小值为$4$, $M(\frac{1}{4},1)$

041014
$x^2=-12y$

021280
$y^2=x$

041015
$y^2=8x$

021304
$\frac{\pi}{2}$

021308
$\frac{11}{2}$

021287
$\frac{45}{8}$

009840
$(\frac{1}{4},0)$;$x=-\frac{1}{4}$

021309
2

021290
$(\frac{1}{2},1)$

021291
$y^2=2x$或$y^2=6x$

041016
相切

021339
$x^2-x+y^2=0(x\neq 0)$

021289
$4\sqrt{3}$

021293
3

021294
$(4,2)$

021295
$-4$

021305
$y^2=\pm 4x$

013106
$[-1,1]$

021292
B

008930
$0$或$-\frac{1}{2}$

008934
$4x-y-15=0$

008922
$y=\frac{1}{4},x>\frac{1}{16}$

021299
2

021300
$2\sqrt{15}$

021321
(1) 定点$(2,0)$;(2) 4

041017
(1) 6; (2) $\frac{1}{32}$

041018
8

021316
$\frac{11}{4}$

021326
8

021319
$y=\pm \frac{\sqrt{3}}{3}x+1$

041019
$\frac{2}{p}$

041020
D

041021
(1) $\frac{5p}{8}$; (2) $-2$;$-\frac{p}{y_0}$

021331
D

041022
C

041023
必要不充分

021334
$y=2x-3,x \leq 2$; $y=2x-3,x \in [1,2]$

021335
$y=-2x^2+8x-4$

021336
$y^2=8x-16$

021337
$x^2+y^2=1$

021338
$3x+y-4=0(x \neq 1)$

021340
$(x-1)^2+(y-2)^2=\frac{1}{9}$

021341
$x+2y-5=0$

021342
$x^2+y^2=4(x>0,y>0)$

021343
$(x-3)^2=10y-15$

041024
C

008846
0或$-\frac{1}{2}$

008847
$\frac{3}{2}$

008852
0或$\frac{1}{4}$或$-\frac{1}{2}$

008853
$[-4,4]]$

041025
(2) $13x-2y=0$

041026
$(-3,5),(1,1)$

041027
$k<-2$或$k>2$或$k=\pm \sqrt{3}$

010704
$(-\frac{2\sqrt{13}}{13},\frac{2\sqrt{13}}{13})$

010703
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

021348
$x^2+4(y-1)^2=4(0 \leq x \leq 2, 1 \leq y \leq 2)$

021349
0

021351
$\frac{\pi}{3}$或$\frac{2\pi}{3}$

041028
$(\frac{3\sqrt{3}}{2},1)$; $\arctan \frac{2\sqrt{3}}{9}$

021352
4

021353
D

041029
$x=a+r\cos \alpha, y=b+r \sin \alpha$ ($\alpha$为参数, $\alpha \in \mathbf{R}$)

021354
(1) $M_1$在曲线$C$上, $M_2$不在曲线$C$上; (2) $a=9$

021355
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$双曲线

009845
$x=\frac{2+\cos \alpha}{2}, y=\frac{\sin  \alpha}{2}$ ($\alpha$为参数, $\alpha \in \mathbf{R}$)

009846
$x=1+9t,y=1+12t$,其中 $t$ 为参数,$t\geq 0$

021358
6

021359
$\sqrt{17}$

021362
$(3\sqrt{2},\sqrt{2})$

021363
最大值7; 最小值$\frac{3\sqrt{15}-4}{4}$

021364
$\sqrt{33}+2\sqrt{6}$

012470
B

041030
B

041031
A

041032
$(-3,-\frac{3\sqrt{5}}{5}) \cup (\frac{3\sqrt{5}}{5},3)$

041033
13

041034
$\frac{1+2\sqrt{21}}{3}$

041035
$y=\pm  1$

041036
$y^2=2x-2$

041037
$7\sqrt{3}$

041038
(1) $C_1$是以$(-4,3)$为圆心,半径为1的圆; $C_2$是椭圆 
$\frac{x^2}{64}+\frac{y^2}{9}=1$; (2) $\frac{8\sqrt{5}}{5}$

041039
(1) $x=1$,$5x-2y-3=0$,$2x-y-1=0$,$2x+y-3=0$;
(2) 点 $T$ 不在曲线 $\Gamma$ 上

ans

041073
(-2,$\dfrac{1}{2}$)

041074
$x-8y=0(x<-\dfrac{8}{15}\sqrt{15}$或$x>\dfrac{8}{15}\sqrt{15}$)

041075
$(-\infty,-1)\cup(1,+\infty)$

041076
$[3+2\sqrt{3},+\infty)$

041077
$2\sqrt{10}$

041078
44

002112
$y^2=4x$

002409
$y^2=-\dfrac{9}{2}x$或$x^2=\dfrac{4}{3}y$

041079
$\pm 2\sqrt{6}$

041080
(5,0)

041081
$\dfrac{23}{24}$

041082
176.0

041083
$|PA|_{\min}=\begin{cases}
    a,0<a\leq1\\
    \sqrt{2a-1},a>1
\end{cases}$

041084
不存在

041085
(1)$m_A=91.5,m_B=90\\(2)S^2_A<S^2_B,A$稳定\\(3)$\dfrac{4}{5}$

041086
(1)$1<a<\sqrt{10}\\(2)l:x=3$或$x=\pm \dfrac{5}{7}\sqrt{7}+3$

041087
(1)$d=2$\\(2)$P$不存在\\(3)$l:x=\pm \sqrt{2}y+2$

002112
$y^2=4x$

002409
$y^2=-\dfrac{9}{2}x$或$x^2=\dfrac{4}{3}y$

041079
$\pm 2\sqrt{6}$

041080
$(5,0)$

041088
$2x\pm \sqrt{3}y-2=0$

003441
$\dfrac{11}{4}$

041089
$2x+y-2=0$

041090
$(2,2)$

041091
1$\quad(\dfrac{1}{9},\dfrac{2}{3})$

041092
$48$

041093
C

041094
$S_{max}=30$此时$P(8,4)$

041095
(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($\dfrac{11+\sqrt{21}}{2},-2-2\sqrt{21})$

041096
$(1)C_2:\dfrac{y^2}{4}-\dfrac{x^2}{3}=1\\(2)p>\dfrac{4}{3}\sqrt{3},\quad \overrightarrow{FA}\cdot \overrightarrow{FB}_{max}=9,\quad$此时$p=2\sqrt{3}$\\(3)$p=2\sqrt{3}$

041097
$(-\infty,-2)$

041098
$\dfrac{1}{2}$

041099
(2)(3)(4)

018928
7

041100
AD,CD

041101
(3)(4)

041102
$\pm 2$

041103
$y^2-\dfrac{x^2}{48}=1\quad(y<0)$

041104
4或2或$\dfrac{3}{2}$

041105
(2)

023553
(1)$\dfrac{17}{45}$\\(2)一级6箱，二级2箱\\(3)预估287.69克

041106
$[\dfrac{1}{3},1)\cup(1,3]$

018949
没有被抓的风险

041107
(1)$\dfrac{x^2}{24}+\dfrac{y^2}{20}=1\\S_{max}=\dfrac{5\sqrt{30}}{4}$

041108
D

041109
C

041110
A

041111
B

041112
$\dfrac{2}{5}\sqrt{10}$

041113
A

030201
B

041114
A

041115
$(\sqrt{3},2)$

041116
$\dfrac{\sqrt{2}}{2}$

041117
(1)$arccos\dfrac{2}{5}\\$(2)正弦值为$\dfrac{\sqrt{15}}{5}\\(3)\dfrac{\pi}{6}$

041118
$l:y-2=\dfrac{118}{143}(x-3)$

041119
$x^2+y^2+x-6y+3=0$

041120
曲线方程为$y^2=48-12x\quad(x\geq3)$及$y^2=4x\quad(x<3)$

041121
$x^2+y^2=7$


ans

012345
D

023233
$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
    \end{cases}$.

023255
(1)略；(2)$a_n=\begin{cases}
    \frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2
\end{cases}$