Question

Please help!
Write the standard form equation of a hyperbola with foci at (0,8) and (0,-8) and eccentricity at 4/3

Answer 1

so far

Answer 2

i did 0+0/2 and -8+8/2 to get the center at (0,0)

Answer 3

\[y ^{2}-x ^{2}=1\]

Answer 4

if e=c/a then c^2=16 and a^2=9

Answer 5

if i use b^2=c^2-a^2

Answer 6

\[b=\sqrt{7} \] and b^2=7

Answer 7

@ganeshie8 @ShailKumar

Answer 8

do you think its correct @ShailKumar?

Answer 9

if e=c/a then c^2=16 and a^2=9. How ?

Answer 10

because e=4/3 if e=c/a then c=4 and c=3 c^2=16 and a^2=9

Answer 11

sorry * a=3

Answer 12

But I can say that c = 8 and a = 6 !

Answer 13

4^2=16 and 3^2=9 though because in standard form we want (x-h)^2 over a^2 and (y-k)^2 over b^2

Answer 14

right?

Answer 15

In e = c/a, you know c = 4/3. but you have two unknowns a and c.

Answer 16

For two unknowns, you need two equations ! right ?

Answer 17

is the center (0,0) correct?
right sorry we just solved one like this!

Answer 18

Center is correct.

Answer 19

We need one more equation two solve for a and c.

Answer 20

What is distance of the center from any of the foci ?

Answer 21

distance between x or y?

Answer 22

oh -8 and 8 duh

Answer 23

-8-0=-8
8-0=8

Answer 24

Right ! Now , the hyperbola is a vertical one.

Answer 25

yep! so its going to be (y-k)^2/a^2-(x-h)^2/b^2 because its parallel to y-axis

Answer 26

Yup, so, c = 8 and since e = c/a ==> a = 6

Answer 27

Find b

Answer 28

how is a=6 again?

Answer 29

b=square root 28 and square root 28 squared is just 28 so b^2=28

Answer 30

Right! Do you understand why a = 6 ?

Answer 31

You got it right.

Answer 32

yay! but no, why is a=6?

Answer 33

e = 4/3, c = 8 , e = c/a so a = 6

Answer 34

so you just multiplied 4x2=8 c=8 and 3x2=6 so a=6?

Answer 35

the way i see it...

Answer 36

Ok, do you understand why c = 8 ?

Answer 37

same thing, you multiplied 4x2=8

Answer 38

wait, no c=8 because its the distance from foci to center

Answer 39

got it, thanks!!!

Answer 40

Yes!

Answer 41

Ok, signing off.. :)