Assuming we can construct parabola, hyperbola geometrically just as circle with compass and ellipses with string. What new things can be constructed can constructed. For, example we can double the cube by using parabola and circle i.e. we can construct cube-root of 2.
For, example Can we do things like trisecting an angle or dividing them into n parts, or construction of heptagon?
EDIT: Thanks for reply. I want to give context for my questions. As a personal project, I want to make a puzzle game or app. The UI allows user to create that any conics that are circle, parabola, ellipse, hyperbola, ruled line. There are various parameters that can used to create these conics. In each puzzle some constructions are needed to solve the problems. I need various geometric results and such. That is the gist of it. Therefore, while gather information around this topics, I also need do devise some of my own results and objectives, to make various problems. I can use some guidance.