Can anyone can help me with this circle exercise?

Question

Determine the center and the radius of the circle equation:

$$2x^2 + 2y^2 - 8x - 12y +8=0$$

Please if you know it tell what should I do with the coefficients of the squares.

Answer 1

You should try to rewrite this like below: $$(x-a)^2+(y-b)^2=R^2$$

for your case first divide whole equation by 2 then your equation will be $x^2+y^2-4x-6y+4=0$ now we have: $(x-2)^2+(y-3)^2=3^2$ so, the center of your circle is $(2,3)$ and its radius is 3.