The directrix of a parabola is x = 4. its focus is (2,6) .

what is the standard form of the parabola?

any on this question?

The equation of a parabola is required from the given directric and focus.

The equation of the parabola is

Directrix =

Focus =

The equation of parabola is given by

The equation of the parabola is .

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Step-by-step explanation:

If you plot the directrix and the focus, you can see that the focus is to the left of the directrix.  Since a parabola ALWAYS wraps itself around the focus, our parabola opens sideways, to the left to be specific.  The formula for the parabola that opens to the left is

We will solve this for x at the end.  The negative is out front because it opens to the left.  If it opened to the right, it would be positive.

The vertex of a parabola is exactly halfway between the focus and the directrix, so our vertex coordinates h and k are (3, 6). P is defined as the distance between the vertex and the directrix, or the vertex and the focus.  Since the vertex is directly between both the directrix and the focus, each distance is the same.  P = 1.  Filling in what we have now:

which simplifies to

Now we will solve it for x.

and

so

3 is greater then both of those numbers