Question

By completing the square, calculate the center and radius of the circle given by the equation 2x2+2y2−10x+4y=8
.(1 point)

center: (2.5,−1)
; radius: 11.25−−−−√


center: (5,−2)
; radius: 2

center: (10,−4)
; radius: 4

center: (3.5,−2)
; radius: 10−−√

Answer 1

Divide by 2: x^2 + y^2 − 5x + 2y = 4.

Complete the square:
(x^2 − 5x + 25/4) + (y^2 + 2y + 1) = 4 + 25/4 + 1
=> (x − 2.5)^2 + (y + 1)^2 = 45/4 = 11.25.

Center = (2.5, −1); radius = sqrt(11.25) = sqrt(45)/2.