The section of a cone whose vertex is P and guiding curve the ellipse (x ^ 2)/(a ^ 2) + (y ^ 2)/(b ^ 2) = 1 x = 0 by the plane x = 0 is a rectangular hyperbola. Show that the locus of P is (x ^ 2)/(a ^ 2) + (y ^ 2 + z ^ 2)/(b ^ 2) = 1.

Question

04-07-2024
Mathematics

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The section of a cone whose vertex is P and guiding curve the ellipse (x ^ 2)/(a ^ 2) + (y ^ 2)/(b ^ 2) = 1 x = 0 by the plane x = 0 is a rectangular hyperbola. Show that the locus of P is (x ^ 2)/(a ^ 2) + (y ^ 2 + z ^ 2)/(b ^ 2) = 1.

Sagot :

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The section of a cone whose vertex is P and guiding curve the ellipse (x ^ 2)/(a ^ 2) + (y ^ 2)/(b ^ 2) = 1 x = 0 by the plane x = 0 is a rectangular hyperbola. Show that the locus of P is (x ^ 2)/(a ^ 2) + (y ^ 2 + z ^ 2)/(b ^ 2) = 1. ​

Sagot :

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The section of a cone whose vertex is P and guiding curve the ellipse (x ^ 2)/(a ^ 2) + (y ^ 2)/(b ^ 2) = 1 x = 0 by the plane x = 0 is a rectangular hyperbola. Show that the locus of P is (x ^ 2)/(a ^ 2) + (y ^ 2 + z ^ 2)/(b ^ 2) = 1.