Question

I'll fan and medal!!! How do you find an equation of a parabola with just knowing the vertex and the directrix?

Answer 1

@iGreen @Joel_the_boss @Conqueror

Answer 2

I don't want an answer, I just want an explanation...

Answer 3

The actual problem is: Find an equation of a parabola with a vertex at the origin and directrix y=-2.5. @iGreen

Answer 4

I know that a is positive because it opens up...

Answer 5

Hint:
Let distance between vertex and directrix = p
If directrix is horizontal, parabola is x^2=4py
If directrix is vertical, parabola is y^2=4px
Note:
1. p is also the distance between the focus and vertex.
2. focus and directrix are on opposite sides of the vertex.
3. focus is always inside the concavity (bowl) of the parabola, and directrix is on the convex side.

Answer 6

wait, isn't the distance between the directrix and vertex c? and a=1/4c?... or am I wrong? @mathmate

Answer 7

I think I'm right... thanks anyways :)

Answer 8

Yes, some call it c, some call it p.
The equation should end up the same.
If the directrix is to the left or below the vertex, the graphs are as shown. If the directrix is above the vertex, or to the right, c (or p) is negative, and the graph needs to be reflected about the x- or the y-axis.

Answer 9

so is the equation y=1/10x^2? @mathmate

Answer 10

Yes, y=(1/10)x^2 to be explicit. Well done!

Answer 11

Thanks :)