Question

What is the equation of the circle with a center at `(4 ,1 )` and a radius of `5`?

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)(4))^2 + (y - color(red)(1))^2 = color(blue)(5)^2`

`(x - color(red)(4))^2 + (y - color(red)(1))^2 = 25`

graph{((x - 4)^2 + (y - 1)^2 - 0.06)((x - 4)^2 + (y - 1)^2 - 25) = 0 [-15, 15, -7.5, 7.5]}