Find an equation of the parabola described.
-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5)
A) $y ^ { 2 } = \frac { 25 } { 36 } x$
B) $y ^ { 2 } = \frac { 25 } { 9 } x$
C) $x ^ { 2 } = \frac { 25 } { 36 } y$
D) $x ^ { 2 } = \frac { 25 } { 9 } y$

Question

Find an equation of the parabola described.
-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5) 
A) $y ^ { 2 } = \frac { 25 } { 36 } x$
B) $y ^ { 2 } = \frac { 25 } { 9 } x$
C) $x ^ { 2 } = \frac { 25 } { 36 } y$
D) $x ^ { 2 } = \frac { 25 } { 9 } y$

Quizplus · Accepted Answer

Since the vertex is at (0, 0) and the axis of symmetry is the x-axis, the parabola opens either up or down, and its equation has the form $y^2 = 4px$. Using the point (9, 5), we substitute to find $p$: $5^2 = 4p(9)$, which simplifies to $25 = 36p$, giving $p = \frac{25}{36}$. Thus, the equation is $y^2 = \frac{25}{9}x$.

Find an Equation of the Parabola Described y2=2536xy ^ { 2 } = \frac { 25 } { 36 } xy2=3625​x

Find an Equation of the Parabola Described $y ^ { 2 } = \frac { 25 } { 36 } x$