An equilateral triangle is inscribed in the parabola y² = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

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Solution

Let OAB be the equilateral triangle inscribed in parabola y² = 4ax.

Let AB intersect the x-axis at point C.

Let OC = k

From the equation of the given parabola, we have

∴The respective coordinates of points A and B are

AB = CA + CB =

Since OAB is an equilateral triangle, OA² = AB².

Thus, the side of the equilateral triangle inscribed in parabola y² = 4 ax is .

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