# What is the equation of the parabola with a focus at (0,0) and a directrix of y= -3?

The equation of the parabola is $y = \frac{1}{6} \cdot {x}^{2} - 1.5$
Vertex is at mid point between focus$\left(0 , 0\right)$and directrix $\left(y = - 3\right)$So vertex is at $\left(0 , - 1.5\right)$ The equation of parabola is$y = a {\left(x - 0\right)}^{2} - 1.5 = a {x}^{2} - 1.5$ Distance(d) of vertex from directrix is 1.5 and we know $d = \frac{1}{4 | a |} \mathmr{and} a = \frac{1}{4 \cdot 1.5} = \frac{1}{6}$Hence the equation of the parabola is $y = \frac{1}{6} \cdot {x}^{2} - 1.5$ graph{1/6*x^2-1.5 [-10, 10, -5, 5]}