Question

What are the coordinates of the center of the circle shown below?

x^2+y^2-8x-10y-8=0

Answer 1

(4,5)

Answer 2

\[x^2+y^2-8x-10y-8=0\]\[x^2-8x+y^2-10y-8=0\]\[(x^2-8x+16)-16+(y^2-10y+25)-25-8=0\]\[(x-4)^2+(y-5)^2-49=0\]Thus the centre of the circle is when x-4=0 and y-5 = 0 ie (x,y) = (4,5).

PS the radius is \[\sqrt{49}=7\]

Answer 3

thank you!