Question

An equilateral triangle is inscribed in the parabola \( y^2 = 4ax \), one of whose vertices is at the vertex of the parabola, the length of each side of the triangle is:

• A. \( \sqrt{5} \)
• B. \( \sqrt{6} \)
• C. \( \sqrt{3} \)
• D. \( 8 \sqrt{3} \)

Hint:

In problems involving triangles inscribed in conic sections, use geometric relations and properties of the conic to find the side lengths.

Answer 1

The Correct Option is D

Step 1: Geometry of the parabola. For an equilateral triangle inscribed in a parabola, the geometry of the triangle and the parabola is used to find the length of the sides.
Step 2: Conclusion. Thus, the length of each side of the triangle is \( 8 \sqrt{3} \).