Problem:
Given the equation $10 x+8 y^2-2 y-5=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Parabola
Equation: $10 x+8 y^2-2 y=5$
Vertex: $\left\{\frac{41}{80},\frac{1}{8}\right\}$
Directrix: $x=\frac{33}{40}$
Focal Parameter: $\frac{5}{8}$
Focus: $\left\{\frac{1}{5},\frac{1}{8}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/28944.txt'}