Question

The diagram shows the broadcast of the radio signals from two transmitters which are the foci of a hyperbola. All points of the hyperbola are 48 miles closer to one transmitter than the other. What is the equation of the hyperbola?

Answer 1

@rational

Answer 2

@terenzreignz

Answer 3

so d1-d2 = 48, right?
that should help you find what a is. I assume O is the origin and it is one of the foci.

Answer 4

the center is at (100, 0), yes?

Answer 5

Yes that's the center.

Answer 6

so c = 200 - 100 = 100, yeah?

Answer 7

Yes

Answer 8

so 100+a - (200-[100-a]) = 48

Answer 9

or 2a = 48 => a = ?

oops. previous should have been
100+a - [200 - (100 + a)] = 48

Answer 10

so would a be 24? In 2a=48=>a=? Divide 48 by 2 and thats 24.

Answer 11

yep. 124 - 76 = 48, right?

Answer 12

76 = 200-124

Answer 13

Yes

Answer 14

so a = 24, c = 100. (h,k) = (100, 0) can you find c?

Answer 15

Hang on a min, let me try

Answer 16

I have 10000=576+b^2. So do I divide 10000 by 576?

Answer 17

isolate b^2 and then take the square root

Answer 18

102.83?

Answer 19

you have to subtract 24^2 from both sides

Answer 20

76=b^2

Answer 21

no, b^2 = 100^2 - 24^2 = 10000 - 576 = 9424

Answer 22

Then take the square root of 9424 ?

Answer 23

to get b

Answer 24

or, just write it as \(\sqrt{9424}\)

Answer 25

97.07

Answer 26

So would the equation be 10000=576+97.07

Answer 27

No.. nevermind, thats not it.

Answer 28

(x-100)^2/576 - y^2/97.07 = 1

Answer 29

Closer?..

Answer 30

sorry, i'm teaching.

\[\frac{ (x-h)^2 }{ a^2 }-\frac{ (y-k)^2 }{ b^2 }=1\]

so yes, closer but like that