The correct equation for a circle centered at (5, -9) with a radius of 12 is:
(x-5)² + (y+9)² = 144
To determine this, remember that the general equation for a circle centered at (h, k) with a radius r is:
(x - h)² + (y - k)² = r²
Substitute the given center (5, -9) and radius of 12 into the equation:
(x - 5)² + (y + 9)² = 12²
(x - 5)² + (y + 9)² = 144
Therefore, the correct equation for this circle is (x - 5)² + (y + 9)² = 144. This equation represents all points that are a distance of 12 units away from the center (5, -9) forming the circle.
