判断参数方程x=[a(1-t²)]/[1+t²] y=﹙2bt﹚/﹙1+t²﹚ (a>0,

设t=tanz
(1-t²)/(1+t²) = (1-tan²z)*cos²z = cos²z - sin²z=cos2z
2t /(1+t²) = 2*tanz*cos²z = 2sinz*cosz = sin2z
x/a = cos2z ,y/b = sin2z
那么(x/a)² + (y/b)² =1,是椭圆方程.