Question

find the centre and radius of the circle with equation given by x^2+3x+y^2-2y-3=0

Answer 1

Just Keep the general equation

ax^2 + by^2 +2gx+2fy+c=0

Answer 2

Centre = (-g,-f)

Answer 3

x^2+3x+y^2-2y-3=0

C( -3/2 , 1)

Answer 4

x^2 + 3x + (9/4) + y^2 - 2y + 1 = 3 + (9/4) + 1
[x+(3/2)]^2 + (y-1)^2 = 25/4

We get centre = (-3/2,1)
Radius = 5/2

Answer 5

radius = sqrt ( g^2 + f^2-C)