What is the Equation of a Parabola with a vertex (0,0)  and a directrix x=4

Asked on by emstavro

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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For this question, you need to know that this parabola opens to the left as the directrix is a vertical line 4 units to the right of the vertex (0,0).  The parabola must open away from the directrix.  From this we are going to use the standard form of an equation that opens to the left which is:

`(y-k)^2 = -4p(x-h)`

where (h,k) represents vertex and p represents distance from vertex to directrix on the axis of symmetry.

This parabola contains:

Vertex of `(0, 0)`

`p = 4` because `x = 4,` the directrix, is 4 units from the vertex of (0,0)

Therefore, when we substitute our values we will have:

`(y-0)^2 = -4(4)(x - 0)` Now we will simplify to get:

`y^2 = -16x`

This is the equation for your parabola

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