Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.
f(x) = −16x2
f(x) = 16x2
f(x) = −one sixteenth x2
f(x) = one sixteenthx2

- anonymous

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- anonymous

@satellite73 @princeharryyy

- anonymous

@pooja195

- anonymous

Ans: f(x) = (-1/16)*(x²)
D.

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## More answers

- anonymous

how did you get that ?

- anonymous

@WhateverYouSay

- anonymous

If the focus is at (0,-4) and the directrix is y = 4 then the vertex of the parabola is midway between these two features at (0,0).
The parabola is thus a downward opening parabola with the standard equation x² = 4cy where c is the distance from the vertex to the focus. In this question, c = -4.

- anonymous

is that the formula that you would use for all parabola equations?

- anonymous

@nono266 can you explain this better?

- anonymous

@ganeshie8

- anonymous

well it say's it's the standard equation. So i am assuming yes...

- anonymous

how do you know which one is 'C'

- princeharryyy

still need help!

- princeharryyy

??? @scenemunster

- anonymous

yes please

- princeharryyy

ok! from the start.

- princeharryyy

should we?

- anonymous

yes how do you do that?

- princeharryyy

The parabola can look like

- princeharryyy

|dw:1438718841051:dw|

- princeharryyy

can u see that. @scenemunster

- princeharryyy

and please if u are interested in learning u must be interactive. or u can just have answers. @scenemunster It's up to you.

- anonymous

yes

- anonymous

i understand

- princeharryyy

let's take a general form. suppose this figure.

- princeharryyy

|dw:1438719011601:dw|

- anonymous

this amkes no sense to me tbh

- anonymous

makes

- princeharryyy

now, In this figure Point B is known as the vertex of the parabola, A is known as the focus, and line D is known as Directrix of the parabola.

- princeharryyy

where C is at the same distance from origin as is the focus of parabola.

- princeharryyy

has, it started making sense @scenemunster

- anonymous

yes

- princeharryyy

great, The general equation of east facing parabola, whose vertex is at (0,0) is y^2 = 4ax

- princeharryyy

are you getting it.

- princeharryyy

where a is the distance from vertex to the focus of the parabola

- anonymous

so (a,o)?

- princeharryyy

as distance being a, and the for every positive x there will be two values of y one negative and the other positive , the parabola is sketched this way. i.e., east facing.

- anonymous

im so confused

- princeharryyy

where

- princeharryyy

?

- anonymous

the east facing parabola

- princeharryyy

|dw:1438719685600:dw|

- princeharryyy

TAKING THIS AS CONVENTION, ARE U COMFORTABLE NOW.

- princeharryyy

@scenemunster ??? please be quick! I don't have much time.

- anonymous

ok so a =4?

- princeharryyy

4 comes in general equation. they made the general equation this way

- princeharryyy

a is some constant which changes it's value according to question.

- anonymous

@amistre64 can you help as well. im sorry im naturally blonde and i dont know XD

- anonymous

so what is the equation like how do i set it up

- princeharryyy

Ok, leave that.

- princeharryyy

for your question.

- princeharryyy

let me make the figure.

- princeharryyy

|dw:1438720085660:dw|

- princeharryyy

where a =-4.
y = -16x^2

- princeharryyy

focus of parabola (0,-4)

- princeharryyy

That means the answer is a

- princeharryyy

@scenemunster

- anonymous

ok. i understand but y would it be a my guess was d

- princeharryyy

wait a second, it won't actually be A or D it would be C,
reason,
general equation,
x^2 = -4by
=> x^2 = -16y, b=4
=>y =-x^2/16

- anonymous

ok. my besty said the same thing

- princeharryyy

@scenemunster , n sorry actually I was explaining the east one so by mistake I told u A earlier.

- princeharryyy

and, later we changed the direction of parabola to south and hence the equation changed. Sorry 'bout that but the answer is C for 100%

- princeharryyy

@scenemunster

- anonymous

ok i got it thank you

- princeharryyy

yw :)

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