What is the equation of the parabola with vertex (0,0) and directrix y=2?

Question

anonymous · Answer

A)y=-1/8x^2 
b)y=1/2x^2 
c)y=1/8x^2 
d)y=-1/2x^2

anonymous · Answer

@IMStuck help?

imstuck · Answer

Ok, I'm here to help you with this!

imstuck · Answer

It's an upside down parabola in the form$$x ^{2}=-4py$$

anonymous · Answer

would it be answer A then?

imstuck · Answer

It looks like this:  I always draw them out, even after all this time, because looking at it on paper is so much easier!  I'm not sure of thee answer yet..I need to still find it!

imstuck · Answer

|dw:1406242784286:dw|

imstuck · Answer

The focus is always the same distance from the vertex as the directrix is.  So if the directrix is at y = 2, then the focus is down two from the vertex at (0, -2).  This is your p value...-2.  Fit it into the equation now:

imstuck · Answer

$$x ^{2}=-4(-2)y$$which comes to$$x ^{2}=8y$$now divide both sides by 8 and get$$\frac{ 1 }{8 }x ^{2}=y$$That's it!

imstuck · Answer

It is A.  I left off the - sign.  Sorry.  Good job!  Yes it is A.

anonymous · Answer

Thank you!! @IMStuck you're awesome

imstuck · Answer

awww....go on......and on and on... ; )