Question

How do you convert `x^2 + y^2 = 16` into polar form?

Answer 1

`\rho^2=16`.

Explanation:

By definition, you pass from `(x,y)` coordinates to `(rho, theta)` coordinates by:

`rho = sqrt(x^2+y^2)`
`theta = arctan(y/x)` ( with some changes depending on the sign of `x` and `y`).

So, in your case, the equation becomes simply `\rho^2=16`. This means that the equation represents all the points with distance `4` from the origin, which is a circumference with radius `4`, centered in the origin.