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

1 Answer
Shwetank Mauria
Jul 29, 2016

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]}

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