Question

What is the standard form equation of the parabola with a vertex at (0,0) and directrix at x= -2?

Answer 1

`x = 1/8y^2`

Explanation:

Please observe that the directrix is a vertical line, therefore, the vertex form is of the equation is:

`x = a(y-k)^2+h" [1]"`

where `(h,k)` is the vertex and the equation of the directrix is `x = k - 1/(4a)" [2]"`.

Substitute the vertex, `(0,0)`, into equation [1]:

`x = a(y-0)^2 + 0`

Simplify:

`x = ay^2" [3]"`

Solve equation [2] for "a" given that `k = 0` and `x = -2`:

`-2 = 0 - 1/(4a)`

`4a = 1/2`

`a = 1/8`

Substitute for "a" into equation [3]:

`x = 1/8y^2 larr` answer

Here is a graph of the parabola with the vertex and the directrix: