CTP: Determine the standard form equation of the circle, the location of the center, and the radius length of the circle.

Question

CTP: Determine the standard form equation of the circle, the location of the center, and the radius length of the circle.

x² + y² + 22x - 2y + 50 = 0

Answer 1

reorganize so x and y terms together and number only on right side of equation

x^2 + 22x + y^2 - 2y = -50

complete squares and add same total to right side

x^2 + 22x + 121 + y^2 - 2y + 1 = -50 + 122

express in factored form to be equation of circle:

(x + 11)^2 + (y-1)^2 = 72

center is (-11,1) radius is sqrt(72) = 6sqrt(2)