Question

How do you find the center and radius of the circle `x^2+y^2-10x-2y+50=49`?

Answer 1

Center is `(5,1)` and radius is `5`

Explanation:

For finding center and radius of a circle `x^2+y^2-10x-2y+50=49`, we should first write it in the form `(x-h)^2+(y-k)^2=r^2`, which is the equation of a circle with center `(h,k)` and radius `r`.

Now `x^2+y^2-10x-2y+50=49`

is equivalent to

`ul(x^2-10x+25)+ul(y^2-2y+1)+50=49+ul(25+1)`

or `(x-5)^2+(y-1)^2=49+25+1-50=25=5^2`

Hence center is `(5,1)` and radius is `5`

graph{x^2+y^2-10x-2y+50=49 [-6, 18, -6, 6]}