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Graph and Differential equations for hyperbolas

by shayaan_musta
Tags: differential, equations, graph, hyperbolas
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shayaan_musta
#1
Oct11-11, 09:21 AM
P: 184
Hello experts!
Hope all of you will be fine.

I have an equation i.e. xy=c
And we all know it is hyperbola.

Now I say "graph some of the hyperbolas xy=c". Then kindly tell me how can we extract more than 1 graph from this single equation? And you will write the differential equations for them. while here only 1 hyperbola is given i.e. xy=c.


If you have any confusion about the question the kindly tell me. I will try to clear more.

Thanks in advance.
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1mmorta1
#2
Oct11-11, 10:56 AM
P: 158
Assuming c is some constant, you have y = c/x. This is a family of graphs, which varies based on values of c. I.E. y = 1/x, y = 2/x, ...y = c/x
shayaan_musta
#3
Oct13-11, 05:12 AM
P: 184
Quote Quote by 1mmorta1 View Post
Assuming c is some constant, you have y = c/x. This is a family of graphs, which varies based on values of c. I.E. y = 1/x, y = 2/x, ...y = c/x
Oh thanks. It is quite helpful.

shayaan_musta
#4
Oct13-11, 11:29 AM
P: 184
Graph and Differential equations for hyperbolas

y[itex]^{2}[/itex]=4ax is also a parabola & and y=[itex]\frac{c}{x}[/itex] too?

Is it?
HallsofIvy
#5
Oct13-11, 02:30 PM
Math
Emeritus
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PF Gold
P: 39,564
Yes, [itex]y^2= 4ax[/itex] would be a family of parabolas, all passing through (0, 0) having different foci.

I'm not sure what your question about y= c/x is. It is the same as xy= c, your original hyperbola system.
shayaan_musta
#6
Oct14-11, 02:55 AM
P: 184
Quote Quote by HallsofIvy View Post
Yes, [itex]y^2= 4ax[/itex] would be a family of parabolas, all passing through (0, 0) having different foci.

I'm not sure what your question about y= c/x is. It is the same as xy= c, your original hyperbola system.
My real question as you can see that, how can you plot some hyperbolas families from general equation i.e. xy=c?

This could be y=c/x and therefore some families will be y=1/x, y=2/x, y=3/x..........so on.
Where c=any arbitrary constant.

Am I right?
HallsofIvy
#7
Oct14-11, 08:33 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,564
Yes, that is exactly what it is saying. They will be parabolas having the x and y axes as asymptotes, passing through (1, c) and (-1, -c), for each number c. Be sure to include some values of c negative and c= 0.
shayaan_musta
#8
Oct14-11, 09:53 AM
P: 184
Quote Quote by HallsofIvy View Post
Yes, that is exactly what it is saying. They will be parabolas having the x and y axes as asymptotes, passing through (1, c) and (-1, -c), for each number c. Be sure to include some values of c negative and c= 0.
As you said c=0 this implies that y=0/x or y=0
Can y=0 be a parabola? Is it so?


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