Question

Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

Answer 1

You need to use the combined distance formula for this problem.
\[\sqrt{(x_2-x_1)+(y_2-y_1)}=\sqrt{(y_2+y_1)}\]

Plug in the focus of (7, 0) into \[(x_1, y_1)\] of the equation.
The equation will now look like this.
\[\sqrt{(x_2-7)+(y_2-0)}=\sqrt{(y_2+y_1)}\]

Lastly, plug in the directrix on the right side of the equation.
\[\sqrt{(x_2-7)+(y_2-0)}=\sqrt{(y_2-7)}\]

Remove the radicals, distribute the y term binomials. Then, simplify and isolate the x terms. Lastly, isolate the y term.

Answer 2

Oh crap, I'm a total ditz. I forgot to add the most important part of the equation. They're supposed to be squared, so the equation has to look like this.

\[\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(y_2+y_1)^2}\]

Answer 3

Here is a thing i just found that may help too.. http://hotmath.com/hotmath_help/topics/finding-the-equation-of-a-parabola-given-focus-and-directrix.html

Answer 4

Each point on the parabola is always equal distance from the focus and the directrix... that is why you set up 2 distance formulas and equate them