Problem:
Given the equation $10 x^2-2 x-10 y^2-7 y+3=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Hyperbola
Equation: $10 \left(x-\frac{1}{10}\right)^2-10 \left(y+\frac{7}{20}\right)^2=-\frac{33}{8}$
Foci: $\left(
\begin{array}{cc}
 \frac{1}{10} & \frac{1}{20} \left(-7-\sqrt{330}\right) \\
 \frac{1}{10} & \frac{1}{20} \left(\sqrt{330}-7\right) \\
\end{array}
\right)$
Eccentricity: $\sqrt{2}$
Center: $\left\{\frac{1}{10},\frac{1}{2} \left(\frac{1}{20} \left(-7-\sqrt{330}\right)+\frac{1}{20} \left(\sqrt{330}-7\right)\right)\right\}$
Asymptotes: $\left\{y=-x-\frac{1}{4},y=x-\frac{9}{20}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/19923.txt'}