In this answer I included the image below of a reflective X-ray telescope. It is made from two elements; the first is concentric shells of glancing (high incidence) angle paraboloidal surfaces, and the second element is the same except that they are hyperboloidal surfaces.
A "Classic" Cassegrain telescope is also a parabolic mirror followed by a hyperbolic mirror, except that the configuration looks very different since for visible light we can use near-normal incidence and are not restricted to high incidence angles.
Question: Despite looking so different, are these basically the same thing? Is the mathematical relationship between the parabolas and the hyperbolas the same in both cases?
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