Question

How do you convert `r=2(cos(theta))^2` into rectangular form?

Answer 1

`=>(x^2+y^2)^3=4x^4`

Explanation:

we know,`x=rcostheta`,,`y=rsintheta`,`r=sqrt(x^2+y^2)`
Given relation is
`r=2(costheta)^2`
multiplying both sides by `r^2` we have
`r^3=2(rcostheta)^2`
putting `rcostheta=x` and,`r=sqrt(x^2+y^2)`, we get
`(x^2+y^2)^(3/2)=2x^2`
`=>(x^2+y^2)^3=(2x^2)^2`
`=>(x^2+y^2)^3=4x^4`

Is it OK?