Algebra and Trigonometry 10th Edition

$y^2=12x$
We are told that the directrix is right of the origin; thus, $p$ is the negative of the distance between the two points. $6^2=(4)(p)(3)$ So, $p=\dfrac{36}{12}=3$ Since the vertex and focus have the same y-coordinate, the parabola must have a horizontal axis. Now, we will write the equation for a parabola that has a vertical axis using the vertex and $p$. $y^2=4px \implies y^2=(4)(3) \times x$ $\implies y^2=12x$