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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