Question

Determine the center of the circle from the equation.

x² -4x +4 +y² +6y +9 =4

A. (2,-3)
B. (0,-3)
C. (-2,3)

Answer 1

A. (2, -3).

Explanation:

The first step is to complete the square on the terms in x and the terms in y:

x² - 4x +4 +y² +6y + 9 =4

= (x - 2)² - 4 + (y + 3)² - 9 + 4 + 9 = 4

= = (x - 2)² + (y + 3)² - 9 + 9 - 4 + 4 = 4

= (x - 2)² - (y + 3)² = 4.

So the centre is at (2, -3).