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修改17961题面

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wangweiye7840 2024-01-29 09:57:06 +08:00
parent c88fdcbc57
commit 0d1c5b3c1e
1 changed files with 3 additions and 2 deletions
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题库0.3/Problems.json
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@ -487940,7 +487940,7 @@
},
"017961": {
"id": "017961",
"content": "从双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的左焦点$F$引圆$x^2+y^2=a^2$的切线, 切点为$T$, 延长$FT$交双曲线右去于点$P$, 若$M$是线段$FP$的中点, $O$为坐标原点, 则$|MO|-|MT|$的值\\blank{50}.",
"content": "从双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的左焦点$F$引圆$x^2+y^2=a^2$的切线, 切点为$T$, 延长$FT$交双曲线右支于点$P$, 若$M$是线段$FP$的中点, $O$为坐标原点, 则$|MO|-|MT|$的值\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) circle (1);\n\\path [domain = -4:4, samples = 100, name path = cr, draw] plot ({sqrt(1+\\x*\\x/3)},\\x);\n\\draw [domain = -4:4, samples = 100] plot ({-sqrt(1+\\x*\\x/3)},\\x);\n\\draw (-2,0) node [below] {$F$} coordinate (F_1);\n\\draw (2,0) node [below] {$F'$} coordinate (F_2);\n\\path [name path = F1P] (F_1) --++ (30:5);\n\\path [name intersections = {of = F1P and cr, by = P}];\n\\draw (P) node [right] {$P$} -- (F_1) (P) -- (F_2);\n\\draw ($(F_1)!0.5!(P)$) node [above] {$M$} coordinate (M) -- (0,0);\n\\draw ($(F_1)!(0,0)!(P)$) node [above left] {$T$} coordinate (T) -- (0,0);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [
"第七单元"
@ -487952,7 +487952,8 @@
"usages": [],
"origin": "高中数学质量测试综合测试05解析几何圆锥曲线试题9",
"edit": [
"20230606\t王伟叶"
"20230606\t王伟叶",
"20240129\t王伟叶"
],
"same": [],
"related": [],