Question

How do you convert `x^2/4 + y^2 = 4` into polar form?

Answer 1

`r=4/(sqrt(cos^2theta+4sin^2theta))`

Explanation:

Let `x=rcostheta` and `y=rsintheta`
then `x^2/4+y^2=4`
`=>` `(r^2cos^2theta)/4+r^2sin^2theta=4`
Simplifying
`r^2cos^2theta+4r^2sin^2theta=16`
`r^2(cos^2theta+4sin^2theta)=16`
`r^2=16/(cos^2theta+4sin^2theta)`
`r=4/(sqrt(cos^2theta+4sin^2theta))`