Problem:
Given the equation $4 x^2+8 x+4 y^2+y-8=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Circle
Equation: $4 (x+1)^2+4 \left(y+\frac{1}{8}\right)^2=\frac{193}{16}$
Radius: $\frac{\sqrt{193}}{8}$
Circumference: $\frac{\sqrt{193} \pi }{4}$
Center: $\left\{-1,-\frac{1}{8}\right\}$
Area Enclosed: $\frac{193 \pi }{64}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/4597.txt'}