Question

Can someone find the radius and center point of x^2+y^2-16x+2y+56=0 (general form)

Answer 1

Center is
`(8,-1)`

Radius is
`3`

Explanation:

To convert from a general form equation to a standard form equation, we must complete the square for each variable to simplify. Make sure to rearrange the equation to complete the square more easily:

`x^2+y^2-16x+2y+56=0\\\\x^2-16x+56+y^2+2y=0\\\\x^2-16x+56(+8)+y^2+2y(+1)=0+8+1\\\\x^2-16x+64+y^2+2y+1=9\\\\(x^2-16x+64)+(y^2+2y+1)=9\\\\(x-8)^2+(y+1)^2=9`

Since the equation of a circle is
`(x-h)^2+(y-k)^2=r^2`, our circle will have a center of
`(h,k)\rightarrow(8,-1)` and a radius of
`r^2=9\rightarrow r=3`.