Find the Parabola with Vertex (4,3) and Directrix x=6 (4,3) x=6

$(4, 3)$ $x = 6$

Since the directrix is horizontal, use the equation of a parabola that opens left or right.

${(y - k)}^{2} = 4 p (x - h)$

Find the distance from the focus to the vertex.

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The distance from the focus to the vertex and from the vertex to the directrix is $| p |$ . Subtract the value of the directrix from the $x$ coordinate of the vertex to find $p$ .

$p = 4 - 6$

Subtract $6$ from $4$ .

$p = - 2$

Substitute in the known values for the variables into the equation ${(y - k)}^{2} = 4 p (x - h)$ .

${(y - 3)}^{2} = 4 (- 2) (x - 4)$

Simplify.

${(y - 3)}^{2} = - 8 (x - 4)$

Find the Parabola with Vertex (4,3) and Directrix x=6 (4,3) x=6

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