Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin.
Directrix: y = 2

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

Question

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: y = 2
​
A) $x ^ { 2 } = - 8 y$
B) $x ^ { 2 } = 8 y$
C) $y ^ { 2 } = - 8 x$
D) $y ^ { 2 } = 8 x$
E) $x ^ { 2 } = - \frac { y } { 8 }$

Quizplus · Accepted Answer

The directrix y = 2 is horizontal, indicating a vertical parabola. Since the vertex is at the origin and the directrix is above the vertex, the parabola opens downwards. The distance from the vertex to the directrix is 2, so the focus is at (0, -2), making $p = -2$. The standard form of a vertical parabola is $x^2 = 4py$, so substituting $p = -2$ gives $x^2 = -8y$.

Find the Standard Form of the Equation of the Parabola x2=−8yx ^ { 2 } = - 8 yx2=−8y

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