Question

Find the radius and centre of the circle:
(a) 3x^2 + 3y^2 + 12x + 18y - 43 = 0

Answer 1

$3x^2 + 3y^2 + 12x + 18y - 43 = 0$

$3(x^2+4x+4)-12+3(y^2+6y+9)-27-43=0$

$3(x+2)^2+3(y+3)^2=82$

$(x+2)^2+(y+3)^2=\frac{82}{3}$

Answer: centre of circle is $(-2,-3)$ and radius is $\sqrt{\frac{82}{3}}$ .