Question

I need help with my math. I will medal and fan I promise! It's four questions and I would greatly appreciate it!

Answer 1

@Nurali ?

Answer 2

@MathMusician ?

Answer 3

need help

Answer 4

In math

Answer 5

yes

Answer 6

@MathMusician

Answer 7

@imqwerty

Answer 8

._. alright

Answer 9

let \(p = \) the distance between the focus and the directrix. (you find it!)
The theory says: the equation is \(y = \frac{x^2}{2p}\).

Answer 10

hold on one sec I'm helping a friend on a question..

Answer 11

it's just \(\frac{x^2}{2p}\) because the focus is on the \(y\)-axis.
If it's not on the \(y\)-axis, make a "shift" and "shift back" after finding the intermediate solution. We'll do that when you're back

Answer 12

okay i'm back for now :)

Answer 13

What is \(p\) in the 1st question ?

Answer 14

this is the first question

Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4.

Answer 15

Yes.
Find \(p=\) the distance between the focus and the directrix.

Answer 16

oh so it's 0

Answer 17

p= 0

Answer 18

that's true only if the focus is on the directrix. Not here. Draw the line and the focus on a piece of paper.

Answer 19

p= 8 ... Correct?

Answer 20

Yes!

Answer 21

Because the definition of the parabola is "set of points lying at equal distance from focus and directrix", you must remember that:
- the vertex of the parabola is always halfway between the directrix and the focus.
-> where is the vertex here?

Answer 22

0

Answer 23

sorry that took me so long I had to chase my dog .__.

Answer 24

Yes.
You are dealing with points in the plane (2 coordinates). You will need both coordinates for the later steps : (0,0) .

Answer 25

so (0,0) and (0,8)

Answer 26

The distance is \(p=8\) (a number). The vertex is a point in the plane: (0,0).

Answer 27

ohh okay

Answer 28

———————————————————————
IF the vertex is (0,0), use the formula: \(y = \frac{x^2}{2p}\).
———————————————————————

It is the case here. => result is: \(y=\frac{x^2}{2\times 8} = \frac{x^2}{16}\).

But it's wrong!! because the parabola goes downwards (it won't cross the dirextrix):


——————————————————————————
If the parabola goes downwards, use \(-p\) instead of \(p\).
——————————————————————————

=> \(y=\frac{x^2}{-16}\).