Find the center and radius of the circle with equation x2 + y2 − 4x + 16y + 4 = 0

center-and-radius
x2-y2-4x-16y-4-0

#1

Find the center and radius of the circle with equation x2 + y2 − 4x + 16y + 4 = 0

Answer:

  1. Get the constant (4) on the other side of the equation.
    x^2 + y^2 - 4x + 16y = -4

  2. Arrange the terms into the format for an equation of a circle.
    (x - h)^2 + (y - k)^2 = r^2

2a. Match up like terms
x^2 - 4x + y^2 +16y = -4

2b. Complete the square
(x^2 - 4x + 4) + (y^2 + 16y + 64) = -4 + 4 + 64

2c. Factor and simplify
(x - 2)^2 + (y + 8)^2 = 8^2

Now it’s in the format for an equation of a circle and you can find your radius and the center.