Question

Find the radius of the circle and the coordinates of its center

Answer 1

`\begin{gathered} \text{The equation of a circle with centre (a,b) and radius, r, is given by the equation:} \\ (x-a)^2+(y-b)^2=r^2 \end{gathered}`
`\begin{gathered} x^2-12x-60=-y^2-4y \\ x^2-12x+y^2+4y=60 \\ By\text{ completing the square for x coefficient and y coefficient, we have:} \\ x^2-12x+36+y^2+4y+4=60+36+4 \\ (x-6)^2+(y+2)^2=100 \\ (x-6)^2+(y+2)^2=10^2 \end{gathered}`

Hence, the radius of the circle is 10, and the coordinates of its centre is (6,-2)