Q.Find the focus and vertex of the parabola $y^2 = 20x$.

A conic section's type is fixed by its eccentricity $e$: the parabola ($e=1$, standard form $y^2=4ax$, focus $(a,0)$, directrix $x=-a$, latus rectum $4a$), the ellipse ($0<e<1$, standard form $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ with $a>b$, foci $(\pm c,0)$, $c^2=a^2-b^2$, $e=c/a$), and the hyperbola ($e>1$, standard form $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$, foci $(\pm c,0)$, $c^2=a^2+b^2$, $e=c/a$). Given any equation alrea …