Question

How do you convert `x^2 + y^2 - 2ax = 0` to polar form?

Answer 1

tHe polar form is `r-2acostheta=0`

Explanation:

To convert a cartesian equation to a polar equation, we use the following.
`x=rcostheta` and `y=sintheta`
`x^2+y^2-2ax=0` `=>` `r^2cos^2theta+r^2sin^2theta-2arcostheta=0`
Simplifying
`r^2-2arcostheta=0`
`r-2acostheta=0`

Answer 2

`r=2acostheta`

Explanation:

Using the pass equations

`{(x=rcostheta),(y=rsintheta):}`

`r^2cos^2theta+r^2sin^2theta-2arcostheta=0` or

`r(r-2acostheta)=0` so we have

`r=0` which is a point at the origin of coordinates and

`r=2acostheta`