Problem:
Given the equation $x^2+4 x+9 y^2-9 y-5=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Ellipse
Equation: $(x+2)^2+9 \left(y-\frac{1}{2}\right)^2=\frac{45}{4}$
Foci: $\left(
\begin{array}{cc}
 -2-\sqrt{10} & \frac{1}{2} \\
 \sqrt{10}-2 & \frac{1}{2} \\
\end{array}
\right)$
Eccentricity: $\frac{2 \sqrt{2}}{3}$
Center: $\left\{-2,\frac{1}{2}\right\}$
Area Enclosed: $\frac{15 \pi }{4}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/36109.txt'}