Circle question?

Question

A circle is defined by the equation x^2 + y^2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the length of the radius

Answer 1

Equation of the circle is x² + y² + 8x + 22y + 37 = 0.

x² + 8x + y² + 22y + 37 = 0

Subtract 37 from each side.

x² + 8x + y² + 22y = -37

To complete the squre add (half cooefficient of x )² ie., 4² = 16 to each side of the expression.

x² + 8x + 16 + y² + 22y = -37 + 16

(x + 4)² + y² + 22y = -21

To complete the squre add (half cooefficient of y )² ie., 11² = 121 to each side of the expression.

(x + 4)² + (y² + 22y + 121) = -21 + 121

(x + 4)² + (y + 11)² = -21 + 121

(x + 4)² + (y + 11)² = 100

Write 100 as 10².

(x + 4)² + (y + 11)² = 10²

The above equation is in the form of (x - h)² + (y - k)² = r² where (h, k) = center and r = radius.

Therefore Center = (-4, -11) and Radius = 10.