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An equilateral triangle is inscribed in the parabola `y^2=4ax` whose vertex is at of the parabola. Find the length of its side.

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To find the length of the side of an equilateral triangle inscribed in the parabola \( y^2 = 4ax \), we can follow these steps: ### Step 1: Understanding the Geometry We know that the vertex of the parabola is at the origin (0,0). An equilateral triangle inscribed in the parabola will have its vertices at points that satisfy the equation of the parabola. ### Step 2: Define the Side Length Let the length of the side of the equilateral triangle be denoted as \( l \). ...
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