过椭圆x^2/25+y^2/9=1的右焦点且倾角为45°的弦AB的长为

题目

过椭圆x^2/25+y^2/9=1的右焦点且倾角为45°的弦AB的长为
A:5 B:6 C:90/17 D:7

答案

F(4,0)
y=x-4
x^2/25+(x-4)^2/9=1
9x^2+25x^2-200x+400=225
34x^2-200x+175=0
A(x1,x1-4) B(x2,x2-4)
|AB|=√2*|x1-4|+|x2-4|
=√2*|x1-x2|
=√2*√△/2
=90/17
选C