Question

已知双曲线x^2/a^2-y^2/b^2=1,设x/a+y/b=t,若以t为参数，求出双曲线的参数方程。

Answer 1

由x^2/a^2-y^2/b^2=1可得（x/a+y/b）（x/a－y/b）＝1
所以x/a－y/b＝1/t,再结合x/a+y/b，可求得x=(t+1/t)a/2, y=(t-1/t)b/2

Answer 2

x^2/a^2-y^2/b^2=1,
x^2/a^2-y^2/b^2=(x/a+y/b)(x/a-y/b)
x/a+y/b=t
x/a-y/b=1/t
x=a(t+1/t)/2
y=b(t-1/t)/2