Question

双曲线4x^2-9y^2=36被点(2,1)平分的弦所在直线方程

Answer 1

y-1=k(x-2)

y=kx+(1-2k)

代入

(4-9k²)x²-18k(1-2k)x-9(1-2k)²-36=0

x1+x2=18k(1-2k)/(4-9k²)

则重点横坐标=(x1+x2)/2=9k(1-2k)/(4-9k²)=2

9k-18k²=8-18k²

k=8/9

所以是8x-9y-7=0