170850
AssignmentMultiple Choice

Conic Sections

Question 170850 • Precalculus

Which equation has a center at (2, 1) and a point on the circle of (2, –3)?

Answer
A
(x + 2)2 + (y + 1)2 = 16
B
(x – 2)2 + (y – 1)2 = 4
C
(x – 2)2 + (y – 1)2 = 16
D
(x + 2)2 + (y + 1)2 = 4

Explanation

A circle with center (h, k) has equation (x − h)² + (y − k)² = r². Using the center (2, 1) gives (x − 2)² + (y − 1)². The point (2, −3) is 4 units from the center, so r² = 4² = 16; choice C matches.

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