Question

Find the standard formula for the hyperbola with vertices at (-7, 0) and (7, 0) and foci at (-9, 0 ) and (9, 0).

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

can someone help me!

Answer 3

So it looks like this hyperbola is centered around (0, 0), which will make things easier.

Answer 4

It also looks like it opens left and right.

Thus, the standard form equation should be:

\[\frac{x^2}{a^2} - \frac{y^2}{b^2}\]

That means we just have to find a and b.

Answer 5

To find a and b, we need to find the distance from the center to the foci. In this case, that's easy: it's 9.

That means that we have:

\[9^2 = a^2 + b^2\]
\[81 = a^2 + b^2\]

Answer 6

thanks so much shadowfiend!! i really appreciate your help

Answer 7

We also have the vertices of the hyperbola. We know the vertices for a hyperbola centered at (0, 0) are: (a, 0) and (-a, 0).

Since the vertices here are (7, 0) and (-7, 0), we know a = 7. Thus, we have:

\[\begin{align}
81 &= 7^2 + b^2\\
81 &= 49 + b^2\\
81 - 49 &= b^2\\
32 &= b^2
\end{align}\]

We don't need b itself, just \(b^2\), for the equation of the hyperbola. We plugin \(a^2\) and \(b^2\) and get:

\[\frac{x^2}{49} - \frac{y^2}{32} = 1\]

Does that all make sense?

Answer 8

yeah that makes sense thanks alot... how do I reward you with a medal?

Answer 9

Click the `good answer' button on the right :)

Answer 10

I'm not seeing a good answer button... sorry I'm new to this site

Answer 11

Damn, really?

Answer 12

could you point it out

Answer 13

Yeah, one sec.

Answer 14

Attached a screenshot showing it.

Let me know if you still can't find it :)

Answer 15

looks like shadow is hulking out :)

Answer 16

thats so strange it doesn't show for me...

Answer 17

That's definitely a problem. tree2193, could you post a screenshot of your screen? I definitely need to see if we can get that fixed.

Answer 18

I WANT YOU TO GET YOUR REWARD MEDAL!!!

Answer 19

yeah sure how do I do that?

Answer 20

Are you running Windows?

Answer 21

yes

Answer 22

hit f5 to refresh the browser and you should see a 'good answer' beside his name

Answer 23

Ok, cool. There should be a button somewhere with the text `prt scrn' or `print screen' or `print scrn' or some variant like that. Hit Alt+that button.

Answer 24

Then open Paint and hit Ctrl-V to paste it, and save that file and post it here.

amistre -- have you run into the good answer button not showing up before?

Answer 25

yep, mostly in internet explorer

Answer 26

Ah. Well that's a doozy :p We will definitely have to take a look at why that's happening.

Answer 27

ok I got it!

Answer 28

f5 tends to cure it tho

Answer 29

I just had to press f5

Answer 30

Ok, cool. Thanks to both of you. We'll see if we can figure out why IE's being silly this time.

And thanks for the medal tree2193!

Answer 31

I have a similar problem if you have time

Answer 32

I probably don't... But post it, and if no one else gets to it in a little while, I'll swing by and check and see what I can do.

Answer 33

ok thanks!

Answer 34

No problem!