Question

How would you find the center and radius of `x^2 + y^2 - 81 = 0`?

Answer 1

Center : `(0,0)`; Radius : `9`.

Explanation:

First, you put the 81 at the right side, you're now dealing with `x^2 + y^2 = 81`.

You now recognize the square of the norm!

`x^2 + y^2 = 81 iff sqrt(x^2 + y^2) = sqrt81 = 9`.

It means that the distance between the origin and any point of the circle has to be equal to 9, you have to see `x^2` as `(x-0)^2` and `y^2` as `(y-0)^2` to see the origin appear. I hope I explained it well.