How do you find the equation of the parabola vertex at the origin and the directrix at x=7?

Jan 10, 2016

With a vertex $= \left(0 , 0\right)$ and directrix $x = 7$, this parabola opens to the left and will be of the form $x = \left(\frac{1}{4 c}\right) {\left(y - k\right)}^{2} + h$

Explanation:

The absolute distance between the directrix and vertex $c = 7 - 0 = 7$

So, the coefficient $\frac{1}{4 c} = \frac{1}{4 \times 7} = \frac{1}{28}$

The sign of the coefficient must be NEGATIVE because the parabola opens to the left.

vertex $= \left(0 , 0\right) = \left(h , k\right)$

Finally, substitute the values into the equation ...

Equation : $x = \left(- \frac{1}{28}\right) {\left(y - 0\right)}^{2} + 0 = - \frac{{y}^{2}}{28}$

hope that helped