Question

Complete the square and then find the center and radius from the circle equation

Answer 1

Center is 2,-4 the radius is 5

Answer 2

Answer:

  center: (2, -4); radius: 5

Step-by-step explanation:

Group x-terms and y-terms. Add the squares of half the coefficient of the linear term in each group. It can be convenient to subtract the constant, too.

  (x^2 -4x) +(y^2 +8y) = 5

  (x^2 -4x +4) +(y^2 +8x +16) = 5 + 4 + 16

  (x -2)^2 +(y +4)^2 = 5^2

Comparing this to the form of a circle centered at (h, k) with radius r, we can find the center and radius.

  (x -h)^2 +(y -k)^2 = r^2

  (h, k) = (2, -4) . . . . . the circle center

  r = 5 . . . . . . . . . . . . the radius