高中的数学题，圆锥曲线20题 高中数学题圆锥曲线20题
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(1)
AD = 2, M(-2, 2λ)
DC = 4, N(-2 + 4λ, 2)
AN: (y - 0)/(2 - 0) = (x + 2)/(-2 + 4λ +2), y = (x+2)/(2λ) (i)
BM: (y -0)/(2λ - 0) = (x - 2)/(-2 - 2), y = -λ(x - 2)/2 (ii)
二者相乘, y² = -(x+2)(x - 2)/4, x²/4 +y² = 1
(2)
令所给点为Q
S = △EGH的面积+△FGH的面积 = (1/2)|GH|*|EQ| + (1/2)|GH|*|QF| = (1/2)|GH|(|EQ|+|FQ|)
= (1/2)|EF|*|GH|
令EF的斜率为k, GH的斜率为-1/k
其余见图
绛旓細濂藉ぇ鐨勫伐绋嬶紝甯屾湜鑳藉府鍒颁綘鍝 鐐瑰嚮涓涓嬪浘鐗囷紝瀹冧細鏀惧ぇ鐨
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