Question

Find the center and the radius of the circle with the equation: x2 - 2x + y2 + 4y + 1 = 0

Answer 1

Complete the square:

x ^2 - 2x + y ^2 + 4y + 1 = 0

(x - 1)^2 + (y + 2)^2 + 1 = 1 + 4

(x - 1)^2 + (y + 2)^2 = 4 = 2^2

Hence the center is (1, -2) and the radius is 2. (D)