Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.
Vertical axis and passes through the point (6,8)

A) $x ^ { 2 } = \frac { 36 } { 8 } y$
B) $y ^ { 2 } = \frac { 8 } { 36 } x$
C) $x ^ { 2 } = \frac { 8 } { 36 } y$
D) $y ^ { 2 } = x$
E) $y ^ { 2 } = \frac { 36 } { 8 } x$

Question

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. 
Vertical axis and passes through the point (6,8)

A) $x ^ { 2 } = \frac { 36 } { 8 } y$
B) $y ^ { 2 } = \frac { 8 } { 36 } x$
C) $x ^ { 2 } = \frac { 8 } { 36 } y$
D) $y ^ { 2 } = x$
E) $y ^ { 2 } = \frac { 36 } { 8 } x$

Quizplus · Accepted Answer

Since the parabola has a vertical axis and the vertex at the origin, its equation is of the form $x^2 = 4py$. Substituting the point (6,8) into this equation, we get $6^2 = 4p(8)$. Solving for $p$ gives $p = \frac{36}{32} = \frac{9}{8}$, so the equation becomes $x^2 = \frac{36}{8}y$, which matches option A.

Find the Standard Form of the Equation of the Parabola x2=368yx ^ { 2 } = \frac { 36 } { 8 } yx2=836​y

Find the Standard Form of the Equation of the Parabola $x ^ { 2 } = \frac { 36 } { 8 } y$