Answer
Ellipse
Work Step by Step
$56{{x}^{2}}-17{{y}^{2}}=234-13{{x}^{2}}-38{{y}^{2}}$
Combine like terms:
$56{{x}^{2}}+13{{x}^{2}}-17{{y}^{2}}+38{{y}^{2}}-234=0$
$69{{x}^{2}}+21{{y}^{2}}-568=0$
Compare the equation $69{{x}^{2}}+21{{y}^{2}}-568=0$ with the standard equation of a conic section $A{{x}^{2}}+B{{y}^{2}}+Cxy+Dx+Ey+F=0$,
Here,
$A=69,B=21$
Here, A and B have the same sign, but $ A \ne B $.
Therefore, the graph of the equation is an ellipse.
