Find an equation of a parabola with a vertex at the origin and directrix y=-2.5

Question

dylanfwlr · Answer

@amistre64

amistre64 · Answer

i always have to do this the long way ....

dylanfwlr · Answer

i dont know any way to do it :/

amistre64 · Answer

y = ax^2  since the vertex is at the origin ... we would need to define 1 point to solve for a

amistre64 · Answer

one thing I do know is that a point that is directly across from the focus has a y value equal to the distance from vertex to directrix;  and an x value that is twice that distance

amistre64 · Answer

so we need to solve for a knowing that the point (5, 2.5) has to be on the parabola

dylanfwlr · Answer

alright

amistre64 · Answer

a = y/x^2

a = 2.5/25

what is the value for a?

dylanfwlr · Answer

1

amistre64 · Answer

i was thinking .1

dylanfwlr · Answer

oh sorry i though 25 was 2.5

amistre64 · Answer

yeah, its hard for these old eyes of mine to see those dots too :)

amistre64 · Answer

so, y = .1 x^2 should do it

dylanfwlr · Answer

that's it?

amistre64 · Answer

http://www.wolframalpha.com/input/?i=y%3D.1x%5E2 the wolf likes it

dylanfwlr · Answer

cool. (i had to change it to a fraction so i just put 1/10)

amistre64 · Answer

thats fine too

amistre64 · Answer

the key is, know where the vertex is, and find that point that is directly across from the focal point.

thats how i do it

dylanfwlr · Answer

there is a few more but i'm going to try them myself before i post

amistre64 · Answer

good luck ;)