Question

How do you convert `r = 6cosθ` into rectangular form?

Answer 1

I found: `x^2+y^2=6x`

Explanation:

Consider the following diagram:

We can see that the relationships between rectangular and polar coordinates are:
`r=sqrt(x^2+y^2)`
`theta=arctan(y/x)`
and:
`x=rcos(theta)`
`y=rsin(theta)`

Given our expression:
`r=6cos(theta)`

multiply by `r` both sides:
`r^2=6rcos(theta)`
so that you get:
`x^2+y^2=6x`
using our relationships of conversion.