Question

Determine the radius and center of the circle with the following equation

x^2+y^2-12x+24y-10=6

Answer 1

Center: (6, -12)

Radius: 4

Explanation:

Complete the squares

`x^2+y^2-12x+24y-10=6\\\\x^2-12x-10+y^2+24y=6\\\\x^2-12x-10+46+y^2+24y+144=6+46+144\\\\(x^2-12x+36)+(y^2+24y+144)=196\\\\(x-6)^2+(y+12)^2=196`

Comparing with the standard form equation
`(x-h)^2+(y-k)^2=r^2`, since
`r^2=196`, then the radius of the circle is
`r=14`. Also, the center of the circle would be
`(h,k)\rightarrow(6,-12)`.