Question

I give medals to helpers thanks
Regan is trying to find the equation of a quadratic that has a focus of (−2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.

Answer 1

can you guys help me plz

Answer 2

y = -1/16(x - (-2))^2 +9.

Answer 3

I dont understand

Answer 4

Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.
Can you give me this answer

Answer 5

HI!!

Answer 6

hi omg can you please help me

Answer 7

no one likes these conic section questions, but they are not that hard really

Answer 8

first off, do you know what the parabola would look like (open right, left, up or down?)

Answer 9

Nope

Answer 10

hmm that is a problem
lets plot the focus and graph the directrix

Answer 11

okay

Answer 12

you can see that the focus \((-2,5)\) is BELOW the directrix, which is a horizontal line
that means the parabola will open DOWN

Answer 13

Ohhh okay

Answer 14

the next thing we need to do is find the vertex
do you know how to find it ?

Answer 15

No ='(

Answer 16

it is the point half way between \((-2,5)\) and \(y=13\)
what is half way between \(5\) and \(13\)?

Answer 17

9

Answer 18

right (got logged out somehow)

Answer 19

that means the vertex is \((-2,9)\)

Answer 20

now we are almost done

Answer 21

OKAY

Answer 22

so now what ?

Answer 23

since the vertex is \((-2,5)\) and it opens down, it will look like
\[4p(y-9)=(x+2)^2\]
all we need is \(p\) and to note that \(4p\) will be negative since it opens down

Answer 24

oops i meant "since the vertex is \((-2,9)\) my mistake

Answer 25

no its -2 5

Answer 26

to find \(p\) is also easy
it is the distance between the focus \((-2,5)\) and the vertex \((-2,9)\)

Answer 27

ohhh n.m.

Answer 28

how far from \(5\) to \(9\)?

Answer 29

did i lose you?