Y^2 = 12X, Find Vertex, Focus , Directrix , Endpoints of the Latus Rectum, and Graph the Parabola.

Step-by-step explanation:

There is a y² term, so the parabola is horizontal.

Vertex-form equation for a horizontal parabola:

x = a(y-k)² + h, where (h,k) is the vertex

If a>0, then

 the parabola opens to the right

 focal length p = 1/(4a)

 focus (h+p,k)

 directrix: x=h-p

 endpoints of latus rectum: (h+p,k±2p)

Put equation into vertex form.

x = (1/12)y²

vertex (0,0)

focal length p = 1/(4·1/12) = 3

focus (0+p,0) = (3,0)

directrix: x = 0-p = -3

endpoints of latus rectum: (3,±6)

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