Question

What is the equation of a circle whose center is at (2,-4) and has a radius of 5 units?

Answer 1

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

Explanation:

Given

`(h,k) = (2,-4)` --- center

`r = 5` --- radius

Required

Determine the equation

The equation of the circle is:

`(x -h)^2 + (y - k)^2 = r^2`

From the given parameters, we have:

`h = 2`

`k = -4`

`r = 5`

So:

`(x -h)^2 + (y - k)^2 = r^2`

`(x - 2)^2 + (y --4)^2 = 5^2`

Express -- as +

`(x - 2)^2 + (y +4)^2 = 5^2`

Evaluate the squares

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