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Asked by g_archanasharma | 28 Mar, 2019, 11:57: AM
answered-by-expert Expert Answer
As shown in figure , equilateral ΔOAB is inscribed in a parabola.
 
Let the coordinates of points A and B be (x1 , y1) and (x1 , -y1)
 
since begin mathsize 12px style angle A O C space end styleis 30°,   ( y1 / x1 ) = tan 30 = 1/√3   or  y1 =  x1/√3
since the point (x1 , y1 ) is on parabola,  y12 = ( x12/3 ) = 4a x1  or  x1 = 12a 
 hence y12 = 4a (12a) = 48a2 or  y1 = 4√3 a
 
hence side of triangle = AB = ( 8√3 a ) units
Answered by Thiyagarajan K | 28 Mar, 2019, 17:52: PM

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