Question

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

Answer 1

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

Explanation:

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

So, the coefficient `1/(4c)=1/(4xx7)=1/28`

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

vertex `=(0,0)=(h,k)`

Finally, substitute the values into the equation ...

Equation : `x=(-1/(28))(y-0)^2+0=-(y^2)/28`

hope that helped