Question

1.求椭圆的方程,x=4+2cosa,y=1+5sina

Answer 1

1.cosa=(x-4)/2 sina=(y-1)/5

两式平方再求和：(x-4)^2/4+(y-1)^2/25=1

2.x-2=t+1/t y-1=t-1/t

两边平方再求差：(x-2)^2-(y-1)^2=4

3.根据(tana)^2+1=(1/cosa)^2

化简得(y+2)^2/9-(x-1)^2/3=1

4.由x=2t有t=x/2,代入y=2t²+1得 y=x^2/2+1