Question

Using the following equation, find the center and radius of the circle. x^2 + 4x + y^2 - 6y= -5

Answer 1

A circle is a set of points in a plane equidistant from a fixed point. It has a general formula of x² + y² = r². This is if the center is at the origin. However, if the center at point h and k, the equation becomes (x-h)² + (y-k)² = r².

We write the given equation in the form (x-h)² + (y-k)² = r² by completing the square.

x² + 4x + y² - 6y = −5
(x² + 4x + 4 )+ (y² - 6y +9) = −5 + 4 + 9 = 8
(x + 2)² + (y + 3)² = (2√2)²

Therefore,

center = (-2, -3)
radius = 2√2