Question

Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

A. (-7, -1), 36 units
B. (7, 1), 36 units
C. (7, 1), 6 units
D. (-7, -1), 6 units

Answer 1

D

Explanation:

To find the center and radius of a circle given its equation, we need to rewrite the equation in the standard form (x - a)^2 + (y - b)^2 = r^2, where (a,b) are the coordinates of the center and r is the radius.

So, let's complete square for x and y terms:

x^2 + 14x + y^2 + 2y + 14 = 0

x^2 + 14x + 49 - 49 + y^2 + 2y + 1 - 1 + 14 = 0

(x + 7)^2 + (y + 1)^2 = 36

Comparing this equation with the standard equation, we get the center at (-7, -1) and radius as sqrt(36) = 6 units.

So, the correct answer is option D: (-7, -1), 6 units.