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Nimfa-mama [501]
3 years ago
15

What are the focus and directrix of the parabola with the equation y=1/12 x^2

Mathematics
1 answer:
Nataly [62]3 years ago
4 0
<h2>Answer:</h2>

\boxed{y=-3}

<h2>Step-by-step explanation:</h2>

The graph of this parabola is shown below. From this graph we know that:

VERTEX:

(h,k)=(0,0)

DIRECTIX:

Since the vertex lies on the origin and the parabola opens upward, then the standard form of this parabola is:

x^2=4py

So:

y=\frac{1}{12}x^2 \\ \\ \therefore 12y=x^2 \ or \ x^2=12y \\ \\ \\ Then: \\ \\ 4p=12 \therefore p=3

Then the directrix is:

y=k-p \\ \\ \therefore y=0-3 \therefore \boxed{y=-3}

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