Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 40

The conic section is a parabola.

Comparing the given equation with the standard equation $$ a x^{2}+b x y+c y^{2}+d x+e y+f=0 $$ we get $a=1,b=-2,c=1$. Now, we check the discriminant $$D=b^2-4ac=4-4= 0$$ Since the discriminant is zero, the conic section is a parabola.