Question

How do you write an equation for a graph whose points vary inversely?

Answer 1

the same way you would make a graph if they didn't very inversely.

do you have the equation?

Answer 2

Question 3-5

Answer 3

so the graphs represent a hyperbola, which is 1 of 4 conic sections.
find the 'general form equation' for a hyperbola in your book for me, then we will continue ^_^

Answer 4

Does this sound right?
c^2=a^2+b^2

Answer 5

mmm..... not quite

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

does this ring a bell? we need to identify what a, b, h, and k are

Answer 6

Okay yeah that was the other one in the book.

Answer 7

and okay. so how do you do that?

Answer 8

so h and k represent the 'center' of the hyperbola, from the looks of the graphs, do you see how the 'center' is (0, 0)?

Answer 9

yes.

Answer 10

so that means (h, k) = (0, 0)
or
h = 0 and
k = 0
for the equation I posted above.
so now all that is left is we need to solve for what 'a' and 'b' are

Answer 11

okay.

Answer 12

so now we have:
\[\frac {x^2}{a^2} - \frac {y^2}{b^2} = 1\]

looking at the first graph, we have:
(1, 2) and (2, 1)

we plug each point into the equation:
\[\frac {1^2}{a^2} - \frac {2^2}{b^2} = 1\]

and
\[\frac {2^2}{a^2} - \frac {1^2}{b^2} = 1\]

Answer 13

ok

Answer 14

what do you do with the bottom part of the equation?

Answer 15

the parts a and b come from the asymtopes

Answer 16

sorry, I gotta take off!
look at the examples and equations in your book! it'll help you finish the questions

Answer 17

so will you work it out then i will have an example for the other 2?

Answer 18

Sorry. Nvm if you have to leave.