What are the focus and directrix of the parabola with the equation y = 1/12 x².

Solution:

The equation of the parabola y = 1/12 x²

Vertex = (0, 0)

Vertex form equation of the parabola is

y = a (x - h)² + k

By comparing the vertex form to the given equation

Vertex (h, k) = (0, 0)

Focus = (h, 1/4a)

h = 0

1/4a = 1 / [4(1/12)] = 3

Focus = (0, 3)

To find the directrix, the given equation can be written as

x² = 12y

By comparing x² = 12y with x² = 4ay

4a = 12

Dividing both sides by 4

a = 3

We know that directrix is written as

y = -a

y = -3

Therefore, the focus and the directrix of the parabola are (0, 3) and y = -3.

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What are the focus and directrix of the parabola with the equation y = 1/12 x².

Summary:

The focus and directrix of the parabola with the equation y = 1/12 x² are (0, 3) and y = -3.