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The standard equation of a circle with center C(h,k) and radius r is as follows:

(x - h)2 + (y - k)2 = r2


(x2 -2hx +h2) + (y2 - 2ky + k2)

We have...

x2 + y2 - 10x + 8y + 5 =0


x2 - 10x + y2 + 8y + 5 =0

add h2 and k2 to both sides

(x2 - 10x + h2) + (y2 + 8y + k2) = -5 + h2 + k2

Using the above framework we can see that 10 = 2h, h = 5
Using the above framework we can see that 8 = 2k, k = 4

So the formula is

(x2 - 10x + 25) + (y2 + 8y + 16) = -5 + 25 + 16

(x - 5)2 + (y - 4)2 = 36

the center of the circle is C(5,4) and radius 6

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Q: Find the center and radius of the circle given by the equation x2 plus y2-10x plus 8y plus 5 equals 0?
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