Question

A circle is defined by the equation x2 + y2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the length of the radius? A. (-4, -10), 11 units B. (-4, -11), 10 units C. (-11, -4), 10 units D. (4, 11), 10 units

Answer 1

standard equation of a circle is (x-h)²+(y-k)²=r², (h, k) is the center of the circle, r is the radius.
rearrange the equation: x²+8x+y²+22y=-37
half of 8 is 4, 4²=16
half of 22 is 11, 11²=121

x²+8x+16+y²+22y+121=-37+16+121
(x+4)²+(y+11)²=100
so the center is at (-4, -11) and the radius is 10. B is the answer.