Let S be the hyperbolic paraboloid with equation z=x y. If p=\l... | Filo
Let S be the hyperbolic paraboloid with equation z=x y. If p=\l... | Filo
4 months ago
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Show that if the point (a, b, c) lies on the hyperbolic paraboloid z=y^2-x^2, then the lines with parametric equations x=a t, y=b t, z=c 2(b-a) t and x=a t y=b-t, z=c-2(b a) t both lie entirely on this paraboloid. (This shows that the hyperbolic paraboloid is what is called a ruled surface; that is, it can be generated by the motion of a straight line. In fact, this exercise shows that through each point on the hyperbolic paraboloid there are two generating lines. The only other quadric surfaces
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