Given ##x^2 + (y – 2)^2 = 4 ## how do you derive a parametric equation?
The parametric equations are ##x=2costheta## and ##y=2+2sintheta##
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##
