The general equation of a circle is (x-h)^2+(y-k)^2=a^2, where a=radius and (h,k) is the centre. So a=3 and we can write (x-h)^2+(y-k)^2=9. If we put x=-1 and y=2 and 8, (-1-h)^2+(2-k)^2=9 and (-1-h)^2+(8-k)^2=9. (-1-h)^2=(1+h)^2. We can substitute for (1+h)^2 between the two equations or subtract the two equations, so (2-k)^2-(8-k)^2=0, so 2-k=8-k or k-8. The only solution is the latter: 2-k=k-8, and 2k=10, so k=5. (1+h)^2+9=9, so h=-1. The equation of the circle is (x+1)^2+(y-5)^2=9. This can be written as a quadratic in x and y: x^2+2x+1+y^2-10y+25=9.
This comes to: x^2+y^2+2x-10y+17=0.
