Problem:
Given the equation $9 x^2-8 y^2-9 y-8=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Hyperbola
Equation: $9 x^2-8 \left(y+\frac{9}{16}\right)^2=\frac{175}{32}$
Foci: $\left(
\begin{array}{cc}
 -\frac{5 \sqrt{119}}{48} & -\frac{9}{16} \\
 \frac{5 \sqrt{119}}{48} & -\frac{9}{16} \\
\end{array}
\right)$
Eccentricity: $\frac{\sqrt{\frac{17}{2}}}{2}$
Center: $\left\{0,-\frac{9}{16}\right\}$
Asymptotes: $\left\{y=\frac{3 x}{2 \sqrt{2}}-\frac{9}{16},y=-\frac{3 x}{2 \sqrt{2}}-\frac{9}{16}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/46660.txt'}