Question

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

Answer 1

Please Help!

Answer 2

@ganeshie8

Answer 3

@thomaster

Answer 4

@amistre64 @norasparkle4 @doggy @xxfaliottaxx @m@Kamille @itsloverboy @UmarsBack @undeadknight26 @elle_girl_0201 @PixieDust1 @Preetha

Answer 5

The equation of the parabola:
y = (1/12)(x - 6)² + 1

Answer 6

Want me to show work?

Answer 7

ocus of the parabola at (6, 4). horizontal line that is 6 units below the focus will be the directrix"
directrix: y = -2

Determine the orientation of the parabola:
The directrix is horizontal, so the parabola is vertical.
The focus lies above the directrix, so the parabola opens upwards.
Equation of up-opening parabola:
 y = a(x - h)² + k

The vertex is halfway between focus and directrix.
vertex (6, 1)
h = 6
k = 1

p = distance between focus and vertex = 3
a = 1/(4p) = 1/12

Answer 8

Thanks ! :)

Answer 9

@roche4321 Any Time :D

Answer 10

Could you help me with another? ;o

Answer 11

@Giobott09

Answer 12

Ya

Answer 13

@Giobott09 but the focus on the question is given at (0,-4).

Answer 14

@mikurout yea but, 1/4 it's, so is negative, so we'll use -1/4 so let's plug all those values in
vertex is at ( 2, -3/4) so distance from the vertex to the focus/directrix(x−2)2=4↑↓−14(y−−34)⟹(x−2)2=−1(y+34)↑vertex coordinates⟹(x−2)2−1=y+34⟹−(x−2)−34=y

Answer 15

@Giobott09 why you will use it as -1/4.
I think it's equation will be
x^2 = -16y
open down.

Answer 16

Bit confused now..

Answer 17

@roche4321 . I am right.

Answer 18

@mikurout You can't be right when u haven't said the answer

Answer 19

@Giobott09 The equation is
x^2 = -16y

Answer 20

@Giobott09 If the vertex is below the x axis would the parabola be shaped like a sad face?

Answer 21

@mikurout Ask the smart one :p

Answer 22

@Giobott09 Not required.

Answer 23

Omg Someone please just say yes or no lol