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AP EAMCET2015MathematicsParabola

An equilateral triangle is inscribed in the parabola y^2=8 x , with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is

Options

  1. A24 3 units
  2. B16 3 units
  3. C8 3 units
  4. D4 3 units

Correct answer

B. 16 3 units

Step-by-step solution

Let a be the length of the side of an equilateral triangle. Then, from above figure, we can say that the point ( 3 2 a, a 2 ) will lie on parabola y^2=8 x . So, ( a 2 )^2=8 ( 3 2 a ) a^2=16 3 a a=16 3 units

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