Question

What is the equation of a circle that has a center at (-4, 10) and a radius of 8?

Answer 1

The equation of the circle is
`(x + 4)^2 + (y - 10)^2 = 64`, third option is correct.

Explanation:

Equation of a circle:

The equation of a circle with center
`(x_0,y_0)` and radius r is given by:

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

Center at (-4, 10)

This means that
`x_0 = -4, y_0 = 10`.

Radius of 8:

This means that
`r = 8`. So

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

`(x - (-4))^2 + (y - 10)^2 = 8^2`

`(x + 4)^2 + (y - 10)^2 = 64`

The equation of the circle is
`(x + 4)^2 + (y - 10)^2 = 64`, third option is correct.