Question

x^2+y^2-2x-10y+2=0 find the circle's center and radius? is the center 1; -5 and the radius is square root 28? just wanted to make sure if i got the correct answer or not

Answer 1

center is (1, 5) and radius is sqrt(24) = 2sqrt(6)

Answer 2

can u explain how did u get sqrt 24

Answer 3

\[x^2+y^2-2x-10y+2=0\]
Start off by completing the square:
\[\left(x^2-2x\right)+\left(y^2-10y\right)+2=0\\
\left(x^2-2x\color{red}{+1}\right)+\left(y^2-10y\color{blue}{+25}\right)+2\color{red}{-1}\color{blue}{-25}=0\\
(x-1)^2+(y-5)^2=24\\(x-1)^2+(y-5)^2=(\sqrt{24})^2\]
Now compare to the general equation of the circle centered at \((h,k)\) with radius \(r\):
\[(x-h)^2+(y-k)^2=r^2\]