Problem:
Given the equation $x-3 y^2+10 y-1=0$, rewrite and classify the conic and state relevant properties.
Answer:
Classification: Parabola
Equation: $x-3 y^2+10 y=1$
Vertex: $\left\{-\frac{22}{3},\frac{5}{3}\right\}$
Directrix: $x=-\frac{89}{12}$
Focal Parameter: $\frac{1}{6}$
Focus: $\left\{-\frac{29}{4},\frac{5}{3}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/conic_sections/29617.txt'}