Problem:
Given the equation $8 x^2-6 x-9 y^2+y+8=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Hyperbola
Equation: $8 \left(x-\frac{3}{8}\right)^2-9 \left(y-\frac{1}{18}\right)^2=-\frac{497}{72}$
Foci: $\left(
\begin{array}{cc}
 \frac{3}{8} & \frac{1}{72} \left(4-\sqrt{8449}\right) \\
 \frac{3}{8} & \frac{1}{72} \left(4+\sqrt{8449}\right) \\
\end{array}
\right)$
Eccentricity: $\frac{\sqrt{\frac{17}{2}}}{2}$
Center: $\left\{\frac{3}{8},\frac{1}{2} \left(\frac{1}{72} \left(4-\sqrt{8449}\right)+\frac{1}{72} \left(4+\sqrt{8449}\right)\right)\right\}$
Asymptotes: $\left\{y=\frac{1}{36} \left(2+9 \sqrt{2}\right)-\frac{2 \sqrt{2} x}{3},y=\frac{2 \sqrt{2} x}{3}+\frac{1}{36} \left(2-9 \sqrt{2}\right)\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/38714.txt'}