Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 39

The conic section is an ellipse.

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 $a=4,b=5,c=7$. Now, we check the discriminant $$D=b^2-4ac=25-112=-87\lt 0$$ Since the discriminant is negative, the conic section is an ellipse.