Question

Write the equation of the hyperbola with the given vertices (-1, 0) and (1,0) and with asymptotes at y = +/-3x

Answer 1

@Vandreigan

Answer 2

Oof, going to make me reach way back for this one. Give me a moment to remember :)

Answer 3

Okay :)

Answer 4

Alright, so first we should find the center of the hyperbola. This is the midpoint between the vertices.

Do you know how to find that?

Answer 5

Center is (0,0)

Answer 6

Excellent :)

Now, we know that the slope of the asymptotes is given by:

Answer 7

\[m = \pm\frac{b}{a}\]

Where a is half the distance between the vertices.

Using this, find a and b.

Answer 8

a = 1
b =

Answer 9

My brain cant function right now haha

Answer 10

How do i find b

Answer 11

Plug in what you know to the equation for the slope of the asymptote.

We know the slope, and we know a. Solve for b.

Answer 12

+/-3x =+/1 b/1 ??

Answer 13

+/-3x =+/-1 b/1 ??*

Answer 14

\[\pm 3 = \pm \frac{b}{1}\]
Which simplifies to:
\[3 = b\]

Answer 15

ohhh okay so b^2 = 9

Answer 16

So, we know a, we know b, and we know where the center is. Do we know which way this hyperbola will open?

Answer 17

You mean if its on the tranverse or conjugate?

Answer 18

Its on transverse

Answer 19

x^2/1 - y^2/9 = 1?

Answer 20

Ok, so we know what equation to plug everything in to.

You're ahead of me. Well done :)

Answer 21

Awesome thanks for all the help :) youre a good teacher!

Answer 22

My pleasure :)