What is an equation of a parabola with a vertex at the origin and directrix x = 4.75?

Solution:

Given, the vertex of the parabola (h, k) = (0, 0)

Directrix, x = 4.75

We have to find an equation of a parabola.

Since, we have x = 4.75 for the directrix, the parabola’s axis of symmetry runs parallel to the x-axis.

The general equation of vertical parabola is

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

Where, (h, k) is the vertex

(h + p, k) is the focus

x = h - p is the directrix.

So, 4.75 = h - p

4.75 = 0 - p

p = -4.75

Now, the equation becomes,

\((y-0)^{2}=4(-4.75)(x-0)\)

\(y^{2}=-19x\)

Therefore, the equation of parabola is \(y^{2}=-19x\).

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What is an equation of a parabola with a vertex at the origin and directrix x = 4.75?

Summary:

An equation of a parabola with a vertex at the origin and directrix x = 4.75 is \(y^{2}=-19x\).