Are you hanging pipe or cable?

PE also has a creep tendency under load so your catenary might get worse over time.

What is the formula and what is "C"?

A drawing would help plus some dimensions, sizes, weights etc

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Also: If you get a response it's polite to respond to it.

On my web site (http://rmniall.com) you will find a downloadable spreadsheet that will do the catenary calculations for you.  It allows for different end elevations, and it allows for (elastic) stretch in the catenary.  Among other things, you can use it to calculate the sag that will result from a given length of unstretched catenary (around the slope from end to end), and it will tell you where the lowest point is.

However, as LittleInch points out, HDPE tends to creep, so you will have to allow for this.

I think you will find a solution in my blog. "C" as you mentioned is lowest position ? You will check the position seeing the catenary graph.

Will a suspended pipe form a catenary curve? I thought a catenary was only for cables, etc. with negligible internal bending strength.

Rod Smith, P.E., The artist formerly known as HotRod10

A suspended pipe will sag; whether that's a shallow catenary, I don't know.

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BridgeSmith - HDPE has a lot of flexibility. Some years back, I was on a construction project and we were installing long runs - >2000' - of pipe. Picking it up was like picking up a piece of spaghetti.

I wasn't contending that the pipe wouldn't bend or sag, just that the deflection would be more like a beam than a cable, which is much simpler to estimate. As I reread the OP, I'm thinking that it may be a pipe supported by a cable, which makes it more complicated than either one. It becomes far less complicated if the pipe is to be held straight, so that the weight of the pipe can assumed to fully carried by the cable.

Rod Smith, P.E., The artist formerly known as HotRod10