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:
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:
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In problems involving triangles inscribed in conic sections, use geometric relations and properties of the conic to find the side lengths.
Updated On: Apr 27, 2026
- \( \sqrt{5} \)
- \( \sqrt{6} \)
- \( \sqrt{3} \)
- \( 8 \sqrt{3} \)
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The Correct Option is D
Solution and Explanation
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 \( 8 \sqrt{3} \).
Step 2: Conclusion. Thus, the length of each side of the triangle is \( 8 \sqrt{3} \).
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