A parabola can be drawn given a focus of (7, -11) and a directrix of y = -3. What can be said about the parabola?

The parabola is negative, with a vertex at (7, -7) and a line of symmetry at x = 7

Step-by-step explanation:

A parabola is set of all points in a plane which are an equal distance away from a given point (focus) and given line (directrix).

Let be any point on the parabola.

Find an equation for the distance between and the focus.  

Find an equation for the distance between and directrix. Equate these two distance equations, simplify, and the simplified equation in and is equation of the parabola.

Distance between and the focus (7, -11):

Distance between and the directrix, y = -3:

Equate the two distance expressions and simplify, making the subject:

This equation in is true for all other values on the parabola so we can rewrite with

Therefore, the equation of the parabola with focus (7, -11) and directrix is y = -3 is:

⇒  (in vertex form)

So the parabola is negative, with a vertex at (7, -7) and a vertical line of symmetry at x = 7

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step-by-step explanation:

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