Question

Using the following equation, find the center and radius: x2 − 4x + y2 + 8y = −4

Answer 1

Hello,

$x^2+4x+y^2+8y=-4\\ x^2-4x+4+y^2+8y+16=-4+4+16\\ \boxed{(x-2)^2+(y+4)^2=4^2}$

center:(2;-4)
Radius=4

Answer 2

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 + 8y = −4
(x² − 4x + 4 )+ (y² + 8y +16) = -4 + 4 + 16 = 16
(x-2)² + (y + 4)² = 4²

Therefore,

center = (2, -4)
radius = 4