# The center of a circle is at (2, −5), and its radius is 12. What is the equation of the circle?

The standard equation of circle is (x − h)^{2} + (y − k)^{2} = r^{2}. Let us use this to find the answer.

## Answer: The equation of a circle that has its center at (2, −5) and has a radius of 12 is (x - 2)^{2} + (y + 5)^{2} = 144.

Let's solve it step by step.

**Explanation:**

Given that, Center (h, k) = (2, -5) and radius (r) = 12.

The equation of a circle with center (h, k) and radius (r) is given by (x − h)^{2} + (y − k)^{2} = r^{2}.

Substitute the values of h, k, r.

(x − 2)^{2} + [y − (-5)]^{2} = 12^{2}

(x − 2)^{2} + (y + 5)^{2} = 144

You can use Cuemath's Equation of Circle Calculator to verify the answer.