Question

双曲线4x方-y方 =4 求以a(2,1)为中点的弦所在直线方程

Answer 1

设A(X1,Y1)

B(X2,Y2)

4x1²-y²=4

4x2²-y2²=4

两式相减得：

4(x1+x2)(x1-x2)-(y1+y2)(y1-y2)=0

x1+x2=4

y1+y2=2

16(x1-x2)-2(y1-y2)=0

k=(y1-y2)/(x1-x2)=8

l:

y-1=8(x-2)

8x-y-15=0