SOLUTION: x^2 + 3y = 0 Whats the focus and directrix?

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Question 961582: x^2 + 3y = 0
Whats the focus and directrix?
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
y=-%281%2F3%29x%5E2
or
x%5E2=-3y

Derive the formula for a parabola and compare.

The derivation uses directrix and focus.

Compare to x%5E2=4py.
-3=4p
p=-3%2F4
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The meaning for p is the distance from directrix or focus to the vertex. The given parabola is inverted, so the vertex is a maximum point with vertical symmetry axis. This one has vertex at the origin, (0,0), as seen from no add or subtract from x and no add or subtract from y. The focus is (0,-3/4) and the directrix is y=3/4.