Question

Write the equation of a parabola with a vertex at (0, 0) and a directrix y = -1.

Answer 1

y = x^2 ?

Answer 2

okay so, either

y = -1/4x^2 or
y = 1/4x^2

its -1/4x^2, eh?

Answer 3

no, pretty sure it will be positive. since the directrix is -1

Answer 4

whaat, really ? strange. i thought for sure it would be negative.

Answer 5

honestly i don't have that much experience with directrix... but from what i googled, the directrix is equidistant from the vertex as the focus is, and the focus is inside the cup of the parabola.

Answer 6

the directrix can't cross the parabola, and y = x^2 stays above the x axis

Answer 7

so if you had y = -1/4x^2, the directrix would intersect with the parabola, which isn't allowed

Answer 8

ohh alright. that makes sense then. so, would you be able to help me with another one super quick? cause i have this question ...

Write the equation of a parabola with a vertex at (0, 0) and a focus at (-4, 0).

and im unfamilar with how to do these as well. =/
once i get like an example i can usually work off of that. (:

Answer 9

this one would be of the form y = -Ax^2

i don't know what A is, i'm sure there's some formula for finding it based off what the focus is

Answer 10

huh. that doesnt help my case. but thanks! haha. ill just have to find an example quick i seeepose.

Answer 11

is your focus (-4, 0) or (0, -4)?

Answer 12

if the focus is (-4, 0) then your equation will be x = -(1/16)y^2

if the focus is (0, 4) then your equation will be y = -(1/16)x^2