- #1
peter.ell
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I'm trying to understand how structures based on conic sections work. For example, when people speak of a parabolic mirror or a parabolic orbit for a satalite, I know what they mean, but when they speak of a hyperbolic mirror or a hyperbolic orbit, what does that actually mean? Is a hyperbolic structure, with the exception of shapes like nuclear power steam vents, just a wider parabola?
Also, what really is the difference between a parabola, half a hyperbola, and a semi-cirlce? If a semi-circe has equal curvature all the way around, and it has a definite center, then why doesn't a circular mirror bring all light to a single focus, while a parabolic mirror can? What's the difference between a center of curvature and a focus?
Thank you so much for helping me. It's been years since I took algebra and none of this was ever explained to me.
Also, what really is the difference between a parabola, half a hyperbola, and a semi-cirlce? If a semi-circe has equal curvature all the way around, and it has a definite center, then why doesn't a circular mirror bring all light to a single focus, while a parabolic mirror can? What's the difference between a center of curvature and a focus?
Thank you so much for helping me. It's been years since I took algebra and none of this was ever explained to me.