Question

Find the co-ordinate of the centre of the circle and it radius if it equation is

1. x^2 +y^2 -10x-12y+6=0

2. -2X^2-2y^2-18y +9=0

Answer 1

1.

$x^2+y^2-10x-12y+6=0.$

$(x-5)^2+(y-6)^2-25-36+6=0.$

$(x-5)^2+(y-6)^2=55.$

Center: $(5,6).$

Radius: $r=\sqrt{55}.$

2.

$-2x^2-2y^2-18y+9=0.$

$x^2+y^2+9y-\frac{9}{2}=0.$

$x^2+(y+\frac{9}{2})^2-\frac{81}{4}-\frac{9}{2}=0.$

$x^2+(y+\frac{9}{2})^2=\frac{99}{4}.$

Center: $(0,-\frac{9}{2}).$

Radius: $r=\frac{3\sqrt{11}}{2}.$