Question

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Answer 1

@phi

Answer 2

First, here is a site with info about a hyperbola
http://www.purplemath.com/modules/hyperbola.htm

Answer 3

do you know the general equation for a hyperbola ?

Answer 4

Not really no.

Answer 5

according to the site
transverse axis is horizontal (in other words, when the center, foci, and vertices line up side by side, parallel to the x-axis), then the a^2 goes with the x part of the hyperbola's equation, and the y part is subtracted.

Answer 6

for the equation scroll down to see it... you want the one that looks like ) ( rather than the smile/frown version

Answer 7

Oh its (x - h)^2/a^2 - (y - k)^2/b^2 = 1.

Answer 8

yes. and (h,k) is the center (see the picture up top, the red dot)

in your problem, they tell you
the hyperbola is centered at (0, 0).
so what is h and k ? if you replace h and k with numbers in the equation, what is the equation?

Answer 9

(h, k) = (0, 0)
(x - 0)^2/a^2 - (y - 0)^2/b^2 = 1

Answer 10

yes, but x-0 is just x and y-0 is y so you have (so far)
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2}= 1 \]

Answer 11

Ok.

Answer 12

they tell you
a vertex 4 inches from the center of the hyperbola

Answer 13

look at the picture up top. can you see where the vertex is? can you figure out either a or b (so we can put them into the equation) ??

Answer 14

The vertexes are the two purple dots. How do i find a and b?

Answer 15

they tell you
a vertex 4 inches from the center of the hyperbola
and you know where the center is.
so where is the vertex ?

Answer 16

remember the center (h, k) = (0, 0)

Answer 17

the vertex is on the x-axis, 4 inches from the center.

Answer 18

4? Im sorry, i dont know. Im so confused... this should be easy but its not.

Answer 19

the vertex is 4 over on the x-axis, so it is at (4,0)
that is where the purple dot is for your problem. If you know the vertex is 4 to the right of the center, can you figure out a or b? Look at the picture...

Answer 20

Is a (4, 3)?

Answer 21

a is just a distance (a single number, not a pair of numbers)

Answer 22

The picture doesnt have numbers on the lines so its kind of confusing.

Answer 23

the picture shows that "a" is the distance between the center and the vertex. What is "a" for your problem ? In other words, how far apart are the points (0,0) and (4,0) ?

Answer 24

4 points away

Answer 25

To the right.

Answer 26

yes, that means a = 4

if you replace a with 4, what is the equation now?

Answer 27

btw, the other vertex is at (-4,0) but we don't need to worry about that side.

Answer 28

x^2/4^2 = y^2/b^2 = 1

Answer 29

too many = signs!

Answer 30

OOps! Sorry i meant x^2/4^2 - y^2/b^2 = 1. Lol

Answer 31

ok, next we use this info they tell us
a focus 1 inch in front of the surface of the mirror

based on the picture, and knowing where our vertex is ( it is at (4,0) ) where is our focus?

Answer 32

On 5? Sorry, i have to go here. Thanks for helping. I may or may not be on later. I hope i didnt waste your time. You did help me get started tho! Which im really grateful for! Thank you! :)

Answer 33

yes the focus is at (5,0)

notice that the distance from the center (0,0) to the focus is labeled c

if you look hard at the site you will find this equation
c^2 - a^2 = b^2

you know c and you know a, so you can find b^2

and that is the last bit of info to put into your equation for the answer.

Answer 34

Yay! Thank you so much!

Answer 35

you should get
5^2 - 4^2 = b^2
or
25 - 16= b^2
9= b^2

so put 9 in for b^2 (or write it as 3^2 which is also 9)