Two poles of height of 50m tied with a rope of 80m since rope is hanging so the lowest hanging point is 10m .Find the distance between the poles

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Zero meters apart.

The interesting thing is that the curve is theoretically still a catenary. If the equation is solved the null answer would show up.

I misread the 10 m as the sag value and got graph.

@Kaustubh , good that you zeroed in on zero.

Yeah, the mid section of the rope is at 40 meters and that's lesser than the length of the pole. 

The thing is - for such questions I always start with unconventional answers. Works out 90% of the times.