Question

What is the equation of the circle with a center at `(5 ,7 )` and a radius of `6`?

Answer 1

See a solution process below:

Explanation:

The equation for a circle is:

`(x - color(red)(a))^2 + (y - color(red)(b))^2 = color(blue)(r)^2`

Where `(color(red)(a), color(red)(b))` is the center of the circle and `color(blue)(r)` is the radius of the circle.

Substituting the values from the problem gives:

`(x - color(red)(5))^2 + (y - color(red)(7))^2 = color(blue)(6)^2`

`(x - color(red)(5))^2 + (y - color(red)(7))^2 = color(blue)(36)`