Question

Determine the radius and center of the circle with the following equation x^2+y^2-12x+24y-10=6

Answer 1

Answer:

Center: (6, -12)

Radius: 4

Step-by-step 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 $(h,k)\rightarrow(6,-12)$.