How do you write a standard form of a parabola with given Focus (4, 3) and Directrix y= -3?

Nov 7, 2016

${\left(x - 4\right)}^{2} = 12 y$

Explanation:

The standard form of equation of parabola is

${\left(x - h\right)}^{2} = 4 p \left(y - k\right)$,

where the focus is $\left(h , k + p\right)$ and the directrix is $y = k - p$.

As focus is $\left(4 , 3\right)$ and directrix is $y = - 3$,

we have $h = 4$ and as $k + p = 3$ and $k - p = - 3$, we have $k = 0$ and $p = 3$.

Hence equation of parabola is ${\left(x - 4\right)}^{2} = 4 \times 3 \times y = 12 y$
graph{((x-4)^2-12y)(y+3)=0 [-5.38, 14.62, -3.92, 6.08]}