Parabolas, Can Anyone Help?

Question

Write the equation of a parabola centered at the origin and with a directrix x = 3.

I had x=(1/12)y^2 and she said check the signs any idea what the right answer is?

2. x=1/-32y^2 and she said check the axis, anybody know?

a = 1/-32 1/-32 = 1/(4p) so -32 = 4p you get p = -8

focus-(-8,0)directrix- x = 8 AOS- y = 0

Answer 1

a parabola does not have any center .. . . i think you mean the vertex.

now.. . .  for the first number, the directrix is to the right of the vertex, thus p is negative

thus

x = (-1/12)y^2

question 2: correct answer.

Answer 2

Note: a can be positive or negative, but p is always positive.

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Directrix x=3 is a vertical line, indicating a horizontal parabola.

Vertex (0,0)

p = 3-0 = 3

Directrix is to the right of vertex  ⇒  parabola opens to the left  ⇒  a<0

a = -1/(4p) = -1/12

http://www.flickr.com/photos/dwread/2799...

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x = (-1/32)y²

vertex (0, 0)

y is the squared term, indicating a horizontal parabola.

axis of symmetry is horizontal and passes through vertex

axis of symmetry y=0

a = -1/32 = -1/(4p)  ⇒  p = 8

a = -1/32 < 0  ⇒   parabola opens left  ⇒  focus lies to the left of vertex; directrix is right of vertex.

focus (0-8, 0) = (-8, 0)

directrix (0+8, 0) = (8, 0)

http://www.flickr.com/photos/dwread/2800...