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 = r2. 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 = r2.

Substitute the values of h, k, r.

(x − 2)2 + [y − (-5)]2 = 122

(x − 2)2 + (y + 5)2 = 144

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

Hence, 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.

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