Write an equation for the parabola vertex 3 5 directrix x 9

Write an equation for the parabola. vertex: (3, -5), directrix: x = 9

The directrix is x = 9

so the parabola is sideways.

which will be of the form :

=> [y - k]² = 4p(x - h)

where (h,k) is a point [vertex] of the parabola.

it is given that h = 3 and k = - 5

therefore [y - (-5)]² = 4p[x - 3]

=> [y + 5]² = 4p[x - 3]

and it is given that directrix is at x = 9

which means that this directrix is 9 units ahead of the vertex (3, - 5)

therefore p = 3 - 9 = - 6

therefore 4p = 4 x -6 = - 24

and so the parabola can be expressed as:

[y + 5]² = -24[x - 3]

which means that the parabola is facing towards left.