Question

(x/a)^2/3

为什么（x/a)^(2/3)+(y/b)^(2/3)=1的参数方程是
x=a*(cost)^3,y=b*(sint)^3

Answer 1

(x/a)^(2/3)+(y/b)^(2/3)=1
((x/a)^(1/3))²+((y/b)^(1/3))²=1
∵ cos²t+sin²t=1
∴ 令(x/a)^(1/3)=cost ,(y/b)^(1/3)=sint
x/a=cos³t ,y/b=sin³t
x=acos²t ,y=bsin³t