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The ellipse x 2 25 + y 2 16 = 1 and the hyperbola x 2 25 - y 2 16 = 1 have ______ in common.

Options

  1. ACenter and vertices only
  2. BCenter, foci and vertices
  3. CCenter, foci and directrices
  4. DCenter only

Correct answer

A. Center and vertices only

Step-by-step solution

For ellipse x 2 25 + y 2 16 = 1 ,   a = 5 and b = 4 Center = 0 ,   0 , vertices ± 5 ,   0 For hyperbola x 2 25 - y 2 16 = 1 ,   a = 5   and b = 4 Center 0 ,   0 , vertices ± 5 ,   0 For ellipse a 2 e 2 = a 2 - b 2 = 25 - 16 = 9 For hyperbola a 2 e 2 = a 2 + b 2 = 25 + 16 = 41 . ∴ Only center and vertices are common.

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