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**richardbird****Member**- Registered: 2006-08-22
- Posts: 1

A bounding curve is formed by the graph lines:

**x = y(a/b) and x = y((a+1)/(b-1))**

**where a and b vary continously over a range say a = 1 to 10, b = 1 to 10.**

What is the equation for the bounding curve? (it resembles x = 1/y)

If the y axis is tilted at 60 degrees to the x axis, (instead of 90 degrees) a 'squashed' curve is formed. What is the equation for the curve with D degrees as a variable parameter?

Is there a name for this family of curves?

Many thanks!

Graphs for the curves are on URL

http://www.richardbird.info/Etch%20segments.htm

*Last edited by richardbird (2006-08-22 02:46:03)*

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,564

Etchilhampton, hmmm... sounds neat.

Also for the right triangles, see pythagorean triples, where q^2 = 2mn.

Because if q^2 is a constant k, then k = 2mn, and n = k/2m, which is a hyperbola.

May just be a coincidence. Not sure if the curve fits your etchilhampton thread-and-nails picture...

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,564

How's this for the 60 degree curve?

x = 1/y + y/2

I haven't graphed it except in my head, so it might be wrong.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,564

Woops, I was wrong.

not y/2 for 60 degrees, try this:

For D degrees, perhaps...

x = 1/y + y tan(90 - D)

**igloo** **myrtilles** **fourmis**

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