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An equilateral triangle is inscribed in the parabola `y^(2)=4ax`, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Text Solution

Verified by Experts

As shown in the figure, equilateral triangle OPQ is symmetrical about x-axis.

Let OP=l.
In triangle OMP,
`OM=OPcos30^(@)=(sqrt(3l))/(2)`
`and Mp=Opsin 3^(@)=(1)/(2)`
`:.p-=((sqrt(3l))/(2),(l)/(2))`
P lies on parabola.
`:." "((l)/(2))^(2)=4a((sqrt(3l))/(2))`
`:." "l=8sqrt(3)a" "rArr" "OP=8sqrt(3)a`
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