Question

How do you convert `r= 9` into cartesian form?

Answer 1

Use the equality `r^2 = x^2 + y^2` to find the converted form
`x^2 + y^2 = 81`

Explanation:

The question How do you convert rectangular coordinates to polar coordinates? has a list of equations used when converting between polar and rectangular systems along with their derivations.

For this problem, we will be using
`r^2 = x^2 + y^2`

If we square both sides of the of `r = 9` we get

`r^2 = 81`

Now we can use the above equality to substitute in `x` and `y` to get

`x^2 + y^2 = 81`

Note that this should make sense intuitively, as `r=9` in polar coordinates is all points of distance `9` from the origin, that is, a circle of radius `9` centered at the origin, and the formula for a circle of radius `s` centered at `(h, k)` in Cartesian coordinates is `(x-h)^2 + (y-k)^2 = s^2`.
Thus a circle of radius `9` centered at the origin would have the formula `(x-0)^2 + (y-0)^2 = 9^2`