Problem:
Given the equation $-10 x^2-4 x-10 y^2+5 y+8=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Circle
Equation: $-10 \left(x+\frac{1}{5}\right)^2-10 \left(y-\frac{1}{4}\right)^2=-\frac{361}{40}$
Radius: $\frac{19}{20}$
Circumference: $\frac{19 \pi }{10}$
Center: $\left\{-\frac{1}{5},\frac{1}{4}\right\}$
Area Enclosed: $\frac{361 \pi }{400}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/34661.txt'}