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

Sagot :

Answer:

Center: (6, -12)

Radius: 4

Step-by-step explanation:

Complete the squares

[tex]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[/tex]

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

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