p^2=cos2a怎样化成直角坐标系的方程

x=pcosa
y=psina
p^2=x^2+y^2
cos2a = 2(cosa)^2-1 = 2x^2/p^2-1 = 2x^2/(x^2+y^2)-1 = (x^2-y^2)/(x^2+y^2)
所以
化成直角坐标系就是：
x^2+y^2 = (x^2-y^2)/(x^2+y^2)
(x^2+y^2)^2 = x^2-y^2

cos2a=2(cosa)^2-1
x=pcosa即cosa=x/p
所以cos2a=2x^2/p^2-1
所以p^2=2x^2/p^2-1
又p^2=x^2+y^2
所以x^2+y^2=2x^2/(x^2+y^2)-1
即(x^2+y^2)^2=x^2-y^2