Write an equation for the parabola with vertex at the origin.
-Through (4, 3), opening to the right
A) $y ^ { 2 } = \frac { 9 } { 4 } x$
B) $y ^ { 2 } = - \frac { 9 } { 4 } x$
C) $x = \frac { 9 } { 4 } y ^ { 2 }$
D) $x ^ { 2 } = \frac { 16 } { 3 } y$

Question

Write an equation for the parabola with vertex at the origin.
-Through (4, 3), opening to the right 
A) $y ^ { 2 } = \frac { 9 } { 4 } x$
B) $y ^ { 2 } = - \frac { 9 } { 4 } x$
C) $x = \frac { 9 } { 4 } y ^ { 2 }$
D) $x ^ { 2 } = \frac { 16 } { 3 } y$

Quizplus · Accepted Answer

The equation of a parabola with vertex at the origin and opening to the right is $y ^ { 2 } = 4 p x$. Substituting the given point (4, 3) into this equation, we get $3 ^ { 2 } = 4 p ( 4 )$, which simplifies to $9 = 16 p$. Solving for $p$, we get $p = \frac { 9 } { 16 }$. Substituting this value of $p$ back into the equation of the parabola, we get $y ^ { 2 } = 4 ( \frac { 9 } { 16 } ) x = \frac { 9 } { 4 } x$.

Write an Equation for the Parabola with Vertex at the Origin