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Graph and Differential equations for hyperbolas 
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#1
Oct1111, 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. 


#2
Oct1111, 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



#3
Oct1311, 05:12 AM

P: 184




#4
Oct1311, 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? 


#5
Oct1311, 02:30 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,552

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. 


#6
Oct1411, 02:55 AM

P: 184

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? 


#7
Oct1411, 08:33 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,552

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.



#8
Oct1411, 09:53 AM

P: 184

Can y=0 be a parabola? Is it so? 


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