Chapter 10 - Section 10.4 - The Parabola; Identifying Conic Sections - Exercise Set - Page 799: 60

Ellipse

Since we are given $x^2=36-4y^2$ It can be written as: $x^2+4y^2-36=0$ Thus, this shows that the variable $x^2$ and $y^2$ are having same signs (but are not equal) so the graph of the given equation is an ellipse.