Chapter 10 - Section 10.4 - The Parabola; Identifying Conic Sections - Exercise Set - Page 799: 61

Circle

Since we are given $3x^2=12-3y^2$ It can be written as: $3x^2+3y^2-12=0$ Thus, this shows that the variable $x^2$ and $y^2$ are having same signs (but the coefficients are equal) so the graph of the given equation is a circle.