Given #x^2 + (y – 2)^2 = 4 # how do you derive a parametric equation?

1 Answer
Dec 19, 2016

The parametric equations are #x=2costheta# and #y=2+2sintheta#

Explanation:

The equation represents a circle, center #(0,2)# and radius #r=2#

We use the following parametric equations

#x=rcostheta#

and #y-2=rsintheta#

Therefore,

#x^2+(y-2)^2=r^2cos^2theta+r^2sin^2theta=4#

So,

#r^2(cos^2theta+sin^2theta)=4#

#r=sqrt4=2#

As #cos^2theta+sin^2theta=1#

The parametric equations are

#x=2costheta# and #y=2+2sintheta#