Unformatted text preview: z = k , we substitute this into the equation of the surface, getting x 2 a 2 + y 2 b 2 = 1 − k 2 c 2 ; to get a nonempty locus, we must have the right side nonnegative, or  k  ≤ c. When we have equality, the intersection is a single point, and otherwise is an ellipse similar to that in ±igure 3.39 , but scaled down: we have superimposed a few of these “sections” of the surface in ±igure 3.39 . To see how these Ft together, we can look at where x y z ±igure 3.39: Horizontal sections...
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 Spring '08
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 Calculus, Rightwing politics, Leftwing politics, Political spectrum

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