Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin.
Focus: (0, $\frac { 1 } { 2 }$ )

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

Question

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (0, $\frac { 1 } { 2 }$ )
​
A) $y ^ { 2 } = - 2 x$
B) $x ^ { 2 } = - 2 y$ ​
C) $y ^ { 2 } = 2 x$
D) $x ^ { 2 } = 2 y$
E) $x ^ { 2 } = \frac { y } { 2 }$

Quizplus · Accepted Answer

The focus of a parabola is a fixed point that, along with the directrix, defines the shape of the parabola. The standard form of a parabola with its vertex at the origin is either $y^2 = 4px$ or $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Given the focus is at $(0, \frac{1}{2})$, this indicates the parabola opens upwards, and $p = \frac{1}{2}$. Therefore, the equation is $x^2 = 2y$, which matches option D.

Find the Standard Form of the Equation of the Parabola 12\frac { 1 } { 2 }21​

Find the Standard Form of the Equation of the Parabola $\frac { 1 } { 2 }$