Find the center and the radius of the circle whose equation is given by x 2 + 4x + y 2 - 8y = 5.

Question

Center and radius

Answer 1

Given equation x^2 + 4x  + y^2 - 8y = 5

x^2 + 4x  + y^2 - 8y - 5  =  0

x^2+ y^2 + 4x  - 8y - 5  =  0

Compare it to circle equation x ^2 + y ^2 + 2gx + 2fy + c = 0.

c  =  - 5

2g  =  4

g  =  2

2f  =  - 8

f  =  - 4

Center =  ( -g , -f )

            =  ( -2 , 4 )

Radius  =  √(g ^2 + f ^2 - c)

             =  √(4 + 16 + 5)

             =  √25

Answer :

Radius of circle( r )  =  5

Center =  ( -2 , 4 )