Answer
True.
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 (or a circle) if $B^2-4AC\lt0$
(iii) defines a hyperbola if $B^2-4AC\gt0$
Hence here the answer since $A=a, B=0, C=6$, hence $B^2-4AC=0^2-4a(6)=-24a$. This must be less than $0$ in order for the conic to be an ellipse, hence $-24a\lt0\\-a\lt0\\a\gt0.$
Hence the statement is true.
