hyperbole folding

[Anonymous]

Hello .
it is not easy to explain what I want to ask but I try.
having a curved line (hyperbole) I want to bend a small piece of it at its center, I don't want to distort that little piece of line but add it to another shape which in this case is a semicircle. with reference to the small segment at the center of the hyperbola highlighted in the drawing, I want to combine two shapes so that the result is different from both the original forms, in other words I want to add two forms that in this case are two curved lines, a small piece of hyperbole with a semicircle to obtain the desired curvature. the aim is to bend a hyperbola in the center maintaining the hyperbolic progression of that small segment.

[Kent1Cooper]

Would you specify the radius [or diameter] of the semi-circle to bend around?  Or would you specify the length along the hyperbola of the part in the middle that bends around a semi-circle, and calculate the size of the semi-circle from that?

Would the bend-around-the-semi-circle part always be exactly in the middle of the length of the hyperbola?  Or would you specify where along it to bend it?

Maybe it wouldn't make any difference, but just in case:  What kind of object is the hyperbola?

[Anonymous]

Hello and thanks. with the first message I created a bit of confusion, I wrote too many inaccurate words, better few and concise. I have to bend a hyperbola in the middle so that two segments are created (as in the attached image) A and B parallel to each other as in the figure. it is obvious that they cannot be perfectly parallel like two straight lines can be. the distance between A and B near the vertex must be 1.5 cm. the small segment at the center which must undergo the semicircle-shaped bending must not be distorted but must maintain the progression of the hyperbola. this time I hope I have explained better.