Why is the secondary mirror in telescopes of the Newtonian system flat, and in the Cassegrain system

Why is the secondary mirror in telescopes of the Newtonian system flat, and in the Cassegrain system it has the shape of a convex hyperboloid?

In a Newtonian telescope, the secondary mirror only turns the light beams (90 °). In the Cassegrain system, the purpose of the secondary mirror is different – to increase the focus. Here, the shape of the secondary mirror should be symmetrical with respect to the main optical axis of the primary mirror.

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