Question

What is the center and radius of the circle with equation `(x - 6)^2 + y^2 = 49`?

Answer 1

Center: `(6, 0)`
Radius: `7`

Explanation:

A circle centered at `(x_0,y_0)` with radius `r` has the equation

`(x-x_0)^2+(y-y_0)^2=r^2`

We can make the given equation fit this form with some slight changes:

`(x-6)^2+y^2 = 49`

`=> (x-6)^2+(y-0)^2 = 7^2`

Thus the circle is centered at `(6,0)` and has radius `7`