Question

点P是双曲线x^2-y^2=1右支上一点,且到直线y-x=0的距离d=根号2,则点P的坐标为

Answer 1

设P(x,y),x>=1由题意|y-x|/√2=√2, |y-x|=2∵y=x是双曲线的渐近线, ∴y=x-2x^2-y^2=x^2-(x-2)^2=4x-4=1, x=5/4, y=x-2=-3/4∴P(5/4,-3/4)