# What is the standard form of the equation of the parabola with a directrix at x=-3 and a focus at (5,3)?

Jan 3, 2016

The Equation of the Parabola is $x = 16 \cdot {y}^{2} - 96 \cdot y + 145$

#### Explanation:

graph{x=16y^2-96y+145 [-10, 10, -5, 5]}

Here the focus is at (5,3) and directrix is x = -3 ; We know the Vertex

is at equidistance from focus and directrix. So the vertex co-

ordinate is at (1,3) and the distance p between vertex and directrix is

$3 + 1 = 4$. We know the equation of parabola with vertex at (1,3)

and directrix at x=-3 is $\left(x - 1\right) = 4 \cdot p \cdot {\left(y - 3\right)}^{2}$ or $x - 1 = 4 \cdot 4 \cdot {\left(y - 3\right)}^{2}$

or $x - 1 = 16 {y}^{2} - 96 y + 144$ or $x = 16 \cdot {y}^{2} - 96 \cdot y + 145$[answer]