# What is the standard form of the equation of the parabola with a directrix at x=-2 and a focus at (-3,3)?

Aug 21, 2016

${\left(y - 3\right)}^{2} = - \left(2 x + 5\right)$, is the reqd. eqn. of Parabola.

#### Explanation:

Let $F \left(- 3 , 3\right)$ be the Focus, and, $d : x + 2 = 0$ the Directrix of the

reqd. Parabola denoted by $S$.

It is known from the Geometry, that, if $P \left(x , y\right) \in S$, then, the $\bot$-

distance btwn. the pt. $P$ & $d$ is the same as the distance btwn.

the pts. $F$ & $P$.

This Property of Parabola is known as the Focus Directrix Property

of Parabola.

$\therefore | x + 2 | = \sqrt{{\left(x + 3\right)}^{2} + {\left(y - 3\right)}^{2}}$

$\therefore {\left(y - 3\right)}^{2} + {\left(x + 3\right)}^{2} - {\left(x + 2\right)}^{2} = 0$

$\therefore {\left(y - 3\right)}^{2} = - \left(2 x + 5\right)$, is the reqd. eqn. of Parabola.