Question 287379
Complete the square in x and y.
{{{x^2+8x+y^2+1y-2=0}}}
{{{(x^2+8x)+(y^2+y)=2}}}
{{{(x^2+8x+16)+(y^2+y+1/4)=2+16+1/4
}}}
{{{(x+4)^2+(y+1/2)^2=8/4+64/4+1/4=73/4}}}
{{{(x+4)^2+(y+1/2)^2=73/4}}}
Compare to the general equation for a circle centered at (h,k) with a radius R:
{{{(x-h)^2+(y-k)^2=R^2}}}
{{{h=-4}}}
{{{k=-1/2}}}
{{{R=sqrt(73)/2}}}