How do you find the center and radius of the circle x^2 + y^2 - 10x - 8y - 8 = 0?

1 Answer
Ratnaker Mehta
Jun 29, 2016

The centre is (5,4), radius r=7.

Explanation:

The given eqn. :x^2+y^2-10x-8y-8=0.
Completing squares on L.H.S., we get,
x^2-10x+25+y^2-8y+16=8+25+16=49.
:. (x-5)^2+(y-4)^2=7^2................(1)

Now the std. eqn. of a circle with centre (h,k) & radius=r is given by,

(x-h)^2+(y-k)^2=r^2

Comparing (1) with the std. eqn, we find that,
the centre is (5,4), radius r=7.

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