Question

Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.

Answer 1

do you know what this looks like
if so it is real easy

Answer 2

i foget what it looks like

Answer 3

lets draw a picture with just the focus and the directrix

Answer 4

the vertex is half way between the focus and the directrix, which is pretty clearly at the origin \((0,0)\)

Answer 5

also from the fact that the focus is below the directrix, the parabola faces down

Answer 6

im following

Answer 7

since the vertex is \((0,0)\) the equation will be
\[4py=-x^2\] and all you need to finish is to find \(p\), the distance between the focus and the vertex

Answer 8

should be more or less obvious that the distance is \(3\) so your equation is
\[12y=-x^2\] or
\[-12y=x^2\] or
\[y=-\frac{x^2}{12}\] or whatever

Answer 9

is the answer y^2= -12x

Answer 10

no

Answer 11

that is why it is important to know what it looks like before you start
if it opens up or down, the \(x\) term is squared, not the \(y\) term

Answer 12

my answer choices are:
y2 = -12x

y2 = -3x

y = negative 1 divided by 12x2

y = negative 1 divided by 3x2

Answer 13

did you see the answers i wrote above? one of them is there

Answer 14

okay it's c y=-1/12 x^2

Answer 15

as always, it is C

Answer 16

haha thx again :)

Answer 17

yw