Question

参数方程x=4+5cost,y=5+5sint怎么消去参数

Answer 1

x-4=5cost,y-5=5sint
(x-4)^2=25cos^2t,(y-5)^2=25sin^2t
(x-4)^2+(y-5)^2=25(cos^2t+sin^2t)
(x-4)^2+(y-5)^2=25
所以图像是一个以（4,5）为圆心，半径为5的圆

Answer 2

由x=4+5cost 得 5cost=x-4 (1)

由y=5+5sint 得 5sint=y-5 (2)

由(1)²+(2)² 得 ( 5cost)²+(5sint)²=(x-4)²+(y-5)²

即 (x-4)²+(y-5)²=25