Question

1.已知双曲线(x^2/9)-(y^2/16)=λ(λ不等于0)经过(9/4 ,5),求该双曲线的实轴长,虚轴长,焦点坐

Answer 1

(9/4)^2/9-5^2/16=λ=-1

(y^2/16)-(x^2/9)=1

实轴长2*4=8

虚轴长2*3=6

焦点坐标(0,±5)

离心率5/4

渐近线方程y=±4/3

设M(t,s),L:y=x+s-t

xx/4+yy=1

xx/4+(x+s-t)^2=1

5/4xx+2(s-t)x+(s-t)^2-1=0

t=(x1+x2)/2

2t=x1+x2=2(t-s)*4/5

s=-1/4t

于是M轨迹y=-1/4x