Problem:
Given the equation $-2 x^2+9 x+2 y^2-7 y+2=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Hyperbola
Equation: $2 \left(y-\frac{7}{4}\right)^2-2 \left(x-\frac{9}{4}\right)^2=-6$
Foci: $\left(
\begin{array}{cc}
 \frac{9}{4}-\sqrt{6} & \frac{7}{4} \\
 \frac{9}{4}+\sqrt{6} & \frac{7}{4} \\
\end{array}
\right)$
Eccentricity: $\sqrt{2}$
Center: $\left\{\frac{9}{4},\frac{7}{4}\right\}$
Asymptotes: $\left\{y=x-\frac{1}{2},y=4-x\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/40195.txt'}