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An equilateral triangle is inscribed in the ellipse whose equation is x 2 + 4 y 2 = 4 . One vertex of the triangle is 0,1 and one altitude is contained in the y -axis. If the length of each side is k 3 units, then k is

Options

  1. A16 13
  2. B8 13
  3. C13 16
  4. D13 8

Correct answer

A. 16 13

Step-by-step solution

x 2 4 + y 2 1 = 1 Equation of A B is y = 3 x + 1 x 2 + 4 3 x 2 + 2 3 x + 1 = 4 ⇒ 13 x 2 + 8 3 x = 0 ⇒ x = - 8 3 13 B C = 16 3 13 units

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