Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - Chapter Review Exercises - Page 639: 49

Equation of the conic section: $x = \frac{1}{{32}}{y^2}$

Referring to Theorem 3 of Section 12.5, this is a parabola where $F = \left( {c,0} \right) = \left( {8,0} \right)$ and directrix $x=-c=-8$. Exchanging $x$ and $y$ in Eq. (9) of Theorem 3 (Section 12.5), we obtain the equation $x = \frac{1}{{4c}}{y^2}$. So, $x = \frac{1}{{32}}{y^2}$.