Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.
Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ; vertical axis

A) $x ^ { 2 } = 75 y$
B) $x ^ { 2 } = - 75 y$
C) $y ^ { 2 } = - 75 x$
D) $y ^ { 2 } = 75 x$
E) $x ^ { 2 } = \frac { y } { 75 }$

Question

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ; vertical axis

A) $x ^ { 2 } = 75 y$
B) $x ^ { 2 } = - 75 y$
C) $y ^ { 2 } = - 75 x$
D) $y ^ { 2 } = 75 x$
E) $x ^ { 2 } = \frac { y } { 75 }$

Quizplus · Accepted Answer

Since the parabola has a vertical axis and the vertex is at the origin, its equation is of the form $x^2 = 4py$. Substituting the point $(-5, \frac{1}{3})$ into this equation gives $(-5)^2 = 4p(\frac{1}{3})$, which simplifies to $25 = \frac{4p}{3}$. Solving for $p$ gives $p = \frac{75}{4}$, so the equation becomes $x^2 = 4(\frac{75}{4})y$ or $x^2 = 75y$.

Find the Standard Form of the Equation of the Parabola (−5,13)\left( - 5 , \frac { 1 } { 3 } \right)(−5,31​)

Find the Standard Form of the Equation of the Parabola $\left( - 5 , \frac { 1 } { 3 } \right)$