Write an equation for the parabola with vertex at the origin.
-Through $( 7,6 )$, opening to the right
A) $x = \frac { 36 } { 7 } y ^ { 2 }$
B) $y ^ { 2 } = - \frac { 36 } { 7 } x$
C) $x ^ { 2 } = \frac { 49 } { 6 } y$
D) $y ^ { 2 } = \frac { 36 } { 7 } x$

Question

Quizplus · Accepted Answer

Since the parabola opens to the right and has its vertex at the origin, its equation is of the form $y^2 = 4px$. Substituting the point (7,6) into this equation, we solve for $p$: $6^2 = 4p(7)$, which simplifies to $36 = 28p$, giving $p = \frac{36}{28} = \frac{9}{7}$. Thus, the equation becomes $y^2 = 4(\frac{9}{7})x = \frac{36}{7}x$, matching option D.

Write an Equation for the Parabola with Vertex at the Origin