Question

The general form of the equation of a circle is x2+y2−4x−8y−5=0. What are the coordinates of the center of the circle?

Answer 1

(2,4)

x^2 + y^2 − 4x − 8y − 5 = 0 complete the square on x and y

( x^2 - 4x + 4) + ( y^2 - 8y + 16) - 5 - 4 - 16 = 0 simplify

(x - 2)^2 + ( y - 4)^2 - 25 = 0 add 25 to both sides

(x - 2)^2 + ( y - 4)^2 = 25

The center is ( 2, 4)

Answer 2

The center of the circle is (2,4)