`x^2=-36y` 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=-36y`

Therefore,

`4p=-36`

`p=-9`

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

Directrix is line with equation `y=9,` focus is the point with coordinates `(0,-9)` and axis of symmetry is `y`-axis.                         

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