Question

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

Answer 1

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`