`x^2=12y` Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

Expert Answers
tiburtius eNotes educator| Certified Educator

Let `x^2=4py` be equation of parabola. Then equation of directrix is `y=-p` coordinates of focus are `(0,p)` and axis of symmetry is `y`-axis.

In this case the equation of parabola is

`x^2=12y`

Therefore,

`4p=12`

`p=3`

Using the facts stated above we can write equation of directrix and coordinates of focus.

Directrix is line with equation `y=-3` focus is the point with coordinates `(0,3)` and axis of symmetry is `y`-axis.                     

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