Problem:
Given the equation $x^2-9 y^2-5 y+6=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Hyperbola
Equation: $x^2-9 \left(y+\frac{5}{18}\right)^2=-\frac{241}{36}$
Foci: $\left(
\begin{array}{cc}
 0 & \frac{1}{18} \left(-5-\sqrt{2410}\right) \\
 0 & \frac{1}{18} \left(\sqrt{2410}-5\right) \\
\end{array}
\right)$
Eccentricity: $\sqrt{10}$
Center: $\left\{0,\frac{1}{2} \left(\frac{1}{18} \left(-5-\sqrt{2410}\right)+\frac{1}{18} \left(\sqrt{2410}-5\right)\right)\right\}$
Asymptotes: $\left\{y=-\frac{x}{3}-\frac{5}{18},y=\frac{x}{3}-\frac{5}{18}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/4351.txt'}