The point (6, -6) lies on a circle centered at (0, 1). Find the equation in standard form. A) x² + (y - 1)² = 85 B) x² + (y + 1)² = 85 C) (x + 1)² + y² = 85 D) (x - 1)² + y² = 85

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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 from the center (0, 1) to the point (6, -6) is sqrt((6-0)^2 + (-6-1)^2) = sqrt(36 + 49) = sqrt(85), so r^2 = 85. Thus, the equation is (x - 0)^2 + (y - 1)^2 = 85, which simplifies to x^2 + (y - 1)^2 = 85.

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