The equation above defines a circle in the xy -plane. What are the coordinates of the center of the circle?

Question

Accepted Answer

Choice B is correct. The standard equation of a circle in the xy -plane is of the form , where are the coordinates of the center of the circle and r is the radius. The given equation can be rewritten in standard form by completing the squares. So the sum of the first two terms, , needs a 100 to complete the square, and the sum of the second two terms, , needs a 64 to complete the square. Adding 100 and 64 to both sides of the given equation yields , which is equivalent to . Therefore, the coordinates of the center of the circle are . Choices A, C, and D are incorrect and may result from computational errors made when attempting to complete the squares or when identifying the coordinates of the center.

Question the-eq