一道椭圆的题 求老师解答 谢谢
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/19 01:38:57
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解题思路: 本题考查了椭圆的标准方程及其性质、直线与椭圆相交问题、有向线段的比值
解题过程:
设A(x1,y1)B(x2,y2)
当m>3,则AB=BP
x2=(x1+m)/2
y2=y1/2 y2^2=y1^2/4
又
x1²/9+y1²/4=1 x1²/36+y1²/16=1/4(1)
x2²/9+y2²/4=1
(x1+m)²/36+y1²/16=1 (2)
(1)(2)消去y得
2mx1+m2=27
x1=(27-m2)/2m
因-3≤x1<3
-3≤(27-m2)/2m<3
得3<m≤9
当0<m<3,AP=2PB
(x1+2x2)=3m/2
y1+2y2=0,y1^2=4y2^2
x1²/9+y1²/4=1 4x1²/9+y1²=4 (3)
x2²/9+y2²/4=1 16x2²/9+4y2²=16 (4)
(3)(4)消去y
8mx2-3m^2=36
x2=(36+3m^2)/8m
因-3≤x2≤3
所以-3≤(36+3m^2)/8m≤3
2≤m<3
综上所述,2≤m<3或3<m≤9
解题过程:
设A(x1,y1)B(x2,y2)
当m>3,则AB=BP
x2=(x1+m)/2
y2=y1/2 y2^2=y1^2/4
又
x1²/9+y1²/4=1 x1²/36+y1²/16=1/4(1)
x2²/9+y2²/4=1
(x1+m)²/36+y1²/16=1 (2)
(1)(2)消去y得
2mx1+m2=27
x1=(27-m2)/2m
因-3≤x1<3
-3≤(27-m2)/2m<3
得3<m≤9
当0<m<3,AP=2PB
(x1+2x2)=3m/2
y1+2y2=0,y1^2=4y2^2
x1²/9+y1²/4=1 4x1²/9+y1²=4 (3)
x2²/9+y2²/4=1 16x2²/9+4y2²=16 (4)
(3)(4)消去y
8mx2-3m^2=36
x2=(36+3m^2)/8m
因-3≤x2≤3
所以-3≤(36+3m^2)/8m≤3
2≤m<3
综上所述,2≤m<3或3<m≤9