The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8 x , with one of its…

 The area (in sq. units) of an equilateral triangle inscribed in the parabola y2=8x, with one of its vertices on the vertex of this parabola is
  1. 643
  2. 2563
  3. 1923
  4. 1283

Solution

 

y2=8x,a=2 

A≡2t2,2(2)t≡2t2,4t

 tan30°=4t2t2=2t=13

 t=23 

Area of ΔOAB=2·ΔOMA=2·12·2t2(4t)=8t3=8(23)3=1923

Asked in: JEE Main 2020 (02 Sep Shift 2)

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