Question 353527
{{{x^2+2x-2y^2-8y=8 }}}
{{{(x^2+2x+1)-2(y^2+4y+4)=8+1-8}}}
{{{(x+1)^2-2(y+2)^2=1}}}
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This is the equation of a hyperbola.
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{{{drawing(300,300,-5,5,-5,5,grid(1),graph(300,300,-5,5,-5,5, -(-1+sqrt(((x+1)^2-1)/2))),
graph(300,300,-5,5,-5,5, -(-1-sqrt(((x+1)^2-1)/2)))),
graph(300,300,-5,5,-5,5,-1-sqrt(((x+1)^2-1)/2))))}}}