Answer
ellipse
Work Step by Step
The general equation of a conic in the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$
(i) defines a parabola if $B^2-4AC=0$
(ii) defines an ellipse if $B^2-4AC\lt0$ and $A\ne C$
(iii) defines a circle if $B^2-4AC\lt0$ and $A= C$
(iv) defines a hyperbola if $B^2-4AC\gt0$
Here $A=10,B=-12,C=4$, hence $B^2-4AC=(-12)^2-4(10)(4)=144-160=-16\lt0$ and $10\ne4$, thus it is an ellipse.
