Parabola Algebra Help! It's Urgent!

Question

1. Write the equation of a parabola centered at the origin and with a focus at the point (0,2).

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

Using the given equations of parabolas, find the focus, the directrix and the equation of the axis of symmetry.

3. y= 1/20 x^2

4. x= 1/-32 y^2

5. x^2 = -8y

Answer 1

Parabolas in this form have the general equation of:

y = 4px^2 (up/down) or

x = 4py^2 (left/right)

where p is the distance from the vertex at (0, 0) and either the focus or the directrix.

So...

1. p = 2, opens up

y = 4(2)x^2

y = 8x^2

2. p = 3, opens left

x = -4(3)y^2 (left/right)

x = -12y^2 (left/right)

3. y= 1/20 x^2 opens up

4p = 1/20

p = 1/80

Focus: (0, 1/80)

Directrix: y = -1/80

Axis: x = 0

4. x= 1/-32 y^2 opens left

4p = 1/32

p = 1/128

Focus: (-1/128, 0)

Directrix: x = 1/128

Axis: y = 0

5. x^2 = -8y

y = -1/8x^2 opens down

4p = 1/8

p = 1/32

Focus: (0, -1/8)

Directrix: y = 1/8

Axis: x = 0

Hope that helps!