Write an equation of the parabola that has a focus at (4, 2) and a directrix at y =-3

Does anybody know how to solve this?? I don't know how you would go about it.

LaughingFace
Apr 26, 2018

#1**+2 **

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Melody
Apr 26, 2018

#3**+1 **

The focus lies above the directrix....so this parabola turns upward

The vertex lies midway between these and is given by ( 4, (2 - 3) / 2 ) = (4, -1/2)

The focal distance,p, is the distance between the vertex and the focus....since the parabola turns upward this is positive and is given by 2 - (-1/2) = 2 + 1/2 = 5/2

So....we have this form :

4p (y - k) = (x - h)^2 where the vertex is (h, k) = (4, -1/2) and p = 5/2

Filling in what we know, we have

4 (5/2) (y - -1/2) = (x - 4 ) ^2

10 ( y +1/2) = ( x - 4 )^2 divide both sides by 10

y +1/2 = (1/10) (x - 4)^2 subtract 1/2 from both sides

y = (1/10) (x - 4)^2 - 1/2 this is in vertex form

CPhill
Apr 26, 2018