双曲线x2/a2-y2/b2=1(a>0,b>0),焦距为2c,直线L过(a,0)和(0,b)
且点(1,0)到直线L的距离与点(-1,0)到直线L的距离之和S≥4/5c.求双曲线的离心率e的取值范围
人气:441 ℃ 时间:2020-04-11 15:08:57
解答
直线方程为:
bx+ay-ab=0
(1,0)和(-1,0)到直线的距离之和:
|b-ab|+|-b-ab|/√a^2+b^2
因为a>0,b>0
|b-ab|+|-b-ab|/√a^2+b^2
=(ab-b+ab+b)/√a^2+b^2
=2ab/√a^2+b^2
>=4/5c
c/a
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