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

1. anonymous

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.

2. anonymous

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. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(y_2+y_1)^2}$

3. DanJS

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

4. DanJS

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

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