Show all work for full credit Exam is worth 120 points but

Show all work for full credit . Exam is worth 120 points, but only has 80 on it: your score will be weighted. Find the radius and center of the following circles. Sketch a graph. (x + 2)^2 + (y - 3)^2 = 9 x^2 +y^2 +4x - 6y - 12 = 0

Solution

Standard equation of circle: ( x- h)^2 + ( y -k)^2 = r^2

where ( h, k) is centre of circle and r is radius.

a) (x+2)^2 + ( y-3)^2 = 9

Comparing with the standard equation of circle: ( h , k) = ( -2 , 3)

radius r = sqrt9 =3

b. x^2 + y^2 +4x -6y -12 =0

( x^2 +4x ) + ( y^2 -6y) -12 =0

(x^2 +4x + 4 -4) + (y^2 -6y +9 -9 ) -12 =0

(x +2)^2 + ( y -3)^2 -4 -9 -12 =0

(x +2)^2 + ( y -3)^2 = 25

Centre ( -2 , 3) and radius = sqrt25 =5