Jaun, you could find the center and radius of the circle by completing the square with each variable.
First of all rearrange the equation in which the x's and y's are added in which is:
4x^2+4x+4y^2-4y-3=0
Factor 4 out of the first two terms and 3rd and 4th terms.
4(x^2+x)+4(y^2-y)-3=0
Complete the square in the two parenthesis containing the x and y variables:
4(x^2+x+(1/2)^2)+4(y^2-y+(1/2)^2)-3+4(1/2)^2+4(1/2)^2=0 Note: the last two terms are added to make the original equation equivelent.
Factor
4(x+1/2)^2+4(y-1/2)^2-3+1+1=0
Collect terms.
4(x+1/2)^2+4(y-1/2)^2 -1=0
4(x+1/2)^2+4(y-1/2)^2=1
Divide the equation by 4.
(x+1/2)^2+(y-1/2)^2=1/4
r^2=1/4 This implies the rudius is r=√(1/4) = 1/2
And the center of the circle is coordinate C(-1/2,1/2).
Hope this helps.
