Question

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

Answer 1

f(x) = −one twelfth (x − 5)2 + 2
f(x) = one twelfth (x − 5)2 + 2
f(x) = −one twelfth (x + 5)2 + 2
f(x) = one twelfth (x + 5)2 + 2

Answer 2

@StudyGurl14 @mjmahmood

Answer 3

yes

Answer 4

can you help?

Answer 5

The equation of a parabola with focus in (h,k+p) and directrix y=k-p, is,
(x-h)^2=4p(y-k)In the first case,
h=-5\\ k+p=-5\\y=k-p=7Combining the last two relations, k=1,p=-6. So the equation of the parabola is,
(x+5)^2=-24(y-1)

Answer 6

did that help

Answer 7

so its the last one?

Answer 8

yes

Answer 9

was it correct

Answer 10

i didnt check it yet

Answer 11

i still need help with 2 more questions

Answer 12

i can help you

Answer 13

Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half.

f(x) = −(x + 2)2 − three fourths
f(x) = (x + 2)2 + three fourths
f(x) = −(x − 2)2 + three fourths
f(x) = −(x − 2)2 − three fourths

Answer 14

Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.

f(x) = one fourthx2 − x + 4
f(x) = −one fourthx2 − x + 4
f(x) = one fourthx2 − x + 5
f(x) = −one fourthx2 − x + 5

Answer 15

so -4(y - 5) = (x - -2)²

Answer 16

The first thing to do is to decide which way up this is and whether its a side ways one or not. Clearly there are 4 different types open up or down or open to the left or right.
The focus is inside the parabola and the directrix is a line on the outside but the same distance from the vertex as the vertex is from the focus.

Because the focus is below the directrix then this is a parabola that opens downwards and has an equation that has an x²
4p(y - k) = (x - h)² is the general form of and opening up or down one

p is the distance from the directrix to the vertex or twice the distance from the directrix to the focus
(h,k) is the co-ords of the vertex

2|p| = 2 so |p| = 1 (the focus is at y = 4 and the directrix is y = 6) difference 2

but because we are facing downwards p = -1

Vertex is at (-2,5) the y co-ord is halfway between the focus and the directrix
The x bit is -2 for the focus and the vertex so the equation becomes

so -4(y - 5) = (x - -2)²

-4(y - 5) = (x + 2)²
-4y +20 = x² +4x + 4
-4y = x² +4x - 16
4y = -x² -4x + 16
y = -1/4x² -x + 4

Answer 17

wait whats the first one?

Answer 18

what do you mean the first one

Answer 19

o i see what you mean thats how to do it

Answer 20

I dont know which one is the answer tho

Answer 21

its either a or b right? @mjmahmood

Answer 22

its d lol

Answer 23

i got 100% thanks!

Answer 24

ok good