# How do you write an equation of a parabola with its vertex at the origin and focus at (0,3)?

Sep 6, 2017

The equation of parabola is $y = \frac{1}{12} {x}^{2}$

#### Explanation:

The standard vertex form of equation of parabola is

 y =a(x-h)^2+k ; (h,k)being vertex , here $h = 0 , k = 0$

The equation of parabola is $y = a {\left(x - 0\right)}^{2} + 0 \mathmr{and} y = a {x}^{2}$

The focus is at $\left(0 , 3\right)$ i.e above the vertex , so parabola

opens upward and $a$ is positive. We know vertex is at

midway between focus and directrix , which is below the vertex.

The distance of directrix from vertex is D=3 and D= 1/(4|a|

$\therefore a = \frac{1}{4 \cdot 3} = \frac{1}{12}$ , So equation of parabola is $y = a {x}^{2}$ or

$y = \frac{1}{12} {x}^{2}$

graph{1/12 x^2 [-10, 10, -5, 5]} [Ans]