The point (6, 0) lies on a circle centered at (-2, 5). Find the equation of the circle in standard form. A) (x + 2)² + (y - 5)² = 89 B) (x + 2)² + (y - 5)² = 64 C) (x - 2)² + (y + 5)² = 89 D) (x - 2)² + (y + 5)² = 64

Question

Quizplus · Accepted Answer

The equation of a circle in standard form is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Given the center (-2, 5) and a point on the circle (6, 0), we can find the radius by calculating the distance between these two points: sqrt((6 - (-2))^2 + (0 - 5)^2) = sqrt(8^2 + 5^2) = sqrt(64 + 25) = sqrt(89). Thus, the equation is (x + 2)^2 + (y - 5)^2 = 89.

The Point (6, 0) Lies on a Circle Centered at (-2