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Hyperbola equation

Posted 9 years ago
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Hi everyone. I have version 10.0.1 of Mathematica. I would like to solve a hyperbola equation of the form Axy+Dx+Ey+F=0 for {x,y} with integer solutions. I've tried it as a y=-(F+Dx)/(Ax+E). Any suggestions?

POSTED BY: Matthew Bennett
2 Replies

With your start, you might proceed as follows. Asymptotically you'll have y=D/A. Try to figure out how large x can be (based on values of {E,F}) before you are in this asymptotic range (because once "close enough", you won't get integer values for y).

POSTED BY: Daniel Lichtblau

The question is a little confusing. Are you trying to find x-y pairs for a range of values of x? Does the code

y[x_]:=-(f+d x)/(a x+e)

do the trick?

POSTED BY: Jason Grigsby
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