The point (-2, -4) lies on a circle centered at (6, 1). Find the equation of the circle in standard form. A) (x + 6)² + (y + 1)² = 89 B) (x - 6)² + (y - 1)² = 89 C) (x - 6)² + (y - 1)² = 7 D) (x + 2)² + (y + 4)² = 89

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Quizplus · Accepted Answer

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. The distance between the center (6, 1) and the point (-2, -4) is the radius, calculated using the distance formula: sqrt((6 - (-2))^2 + (1 - (-4))^2) = sqrt(8^2 + 5^2) = sqrt(64 + 25) = sqrt(89). Thus, the equation is (x - 6)^2 + (y - 1)^2 = 89.

The Point (-2, -4) Lies on a Circle Centered at (6