# What is the standard form of the equation of the parabola with a directrix at x=-8 and a focus at (-7,3)?

Apr 29, 2016

${\left(y - 3\right)}^{2} = - 4 \left(\frac{15}{2}\right) \left(x - \frac{1}{2}\right)$

#### Explanation:

The directrix is x = 8 the focus S is (-7, 3), in the negative direction of x-axis, from the directrix..

Using the definition of the parabola as the locus of the point that is equdistant from the directrix and the focus, its equation is

$\sqrt{{\left(x + 7\right)}^{2} + {\left(y - 3\right)}^{2}} = 8 - x , > 0$,

as the parabola is on the focus-side of the directrix, in the negative x-direction.

Squaring, expanding and simplifying, the standard form is.

${\left(y - 3\right)}^{2} = - 4 \left(\frac{15}{2}\right) \left(x - \frac{1}{2}\right)$.

The axis of the parabola is y = 3, in the negative x-direction and the vertex V is (1/2, 3). The parameter for size, a = 15/2.,