Yes my code runs for me also using Maple 2020. But the graph that I take is not the graph that we need to take! In the picture is a different graph!

Thank you very much! But which comand should I use to take a common graph for different values of C. For example how to get the curves for the values of C 100, 200 and 600 respectively in the same graph? 

Yes the firtst r2 in the equation is meant to be r1! This is a typo. But for C=200, how can we show the intersection of the left hand side of this equation with the right hand side?. This graph that you took as a result is a 3D-graph. We want to take a 2D-Graph.

@Rouben Rostamian  

Excellent! Is there any way to insert to the graph the name of the vectors? (ξ⁰ , η⁰ , φ)

@Rouben Rostamian  

1.I thought that my functions agree with my picture. My goal is to get this picture with the corresponding vectors in maple.

2. I have somehow to change my vectors.

3 Yes there are infinitely lines φ=const. It is not a problem. Let's say that we want to get this graph in Maple taking into account the line φ=π/4. If there are anotherway rathr than using Student:-Vector Calculus, then which is that way?

@Carl Love Yes! It's ok but....The problem is not only to get the two paraboloidals, but also to include the corresponding vectors. In the picture the line (φ=const) is included and the vectors I got by my code (these vectors that are also in the graph that Rouben showed) are not the same as in the picture!

@Rouben Rostamian  The problem is not only get the two paraboloidals, but also to include the corresponding vectors. In the picture the line (φ=const) is included and the vectors I got(these vectors that are also in the graph that you show) are not the same as in the picture!

@acer  In the picture the vectors are different from these that I got! Also in the picture included the line (φ=const)

This is not our graph!!!! In the picture we have two paraboloidal surfaces!!! This is only the left! The code I wrote gives as a result these two paraboloidal surfaces separently. I want to take a graph as shown in the pictures with the corresponding vectors. And the command ''dispay'' doesn't work!

No! Unfortunately plots:-display(LH, LG) doesn't work!!!