Question 285163
Complete the square in x and y.
{{{x^2 + y^2 -4x + 8y = 24}}}
{{{x^2-4x + y^2+8y = 24}}}
{{{(x^2-4x+4) + (y^2+8y+16) = 24+4+16}}}
{{{(x-2)^2 + (y+4)^2 = 44}}}
Compare to the general equation for a circle centered at (h,k) with a radius R:
{{{(x-h)^2+(y-k)^2=R^2}}}
This circle is centered at (2,-4) and has a radius of {{{sqrt(44)=2*sqrt(11)}}}.