Answer
Circle
Work Step by Step
$3{{x}^{2}}+5{{y}^{2}}+{{x}^{2}}={{y}^{2}}+49$
Combine like terms:
$3{{x}^{2}}+{{x}^{2}}+5{{y}^{2}}-{{y}^{2}}=49$
$\begin{align}
& 4{{x}^{2}}+4{{y}^{2}}=49 \\
& {{x}^{2}}+{{y}^{2}}=\frac{49}{4}
\end{align}$
Compare the equation ${{x}^{2}}+{{y}^{2}}=\frac{49}{4}$ with the standard equation of a conic section, $A{{x}^{2}}+B{{y}^{2}}+Cxy+Dx+Ey+F=0$,
Here,
$A=1,B=1$
Since A=B, we find that this is a circle equation.
Therefore, the graph of the equation is a circle.
