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

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Answer 1 · 2016-08-21T18:38:08

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

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

reqd. Parabola denoted by $S$ $S$ .

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

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

the pts. $F$ $F$ & $P$ $P$ .

This Property of Parabola is known as the Focus Directrix Property

of Parabola.

$:. |x+2|=sqrt{(x+3)^2+(y-3)^2}$

$:. (y-3)^2+(x+3)^2-(x+2)^2=0$

$:. (y-3)^2=-(2x+5)$ , is the reqd. eqn. of Parabola.