The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8x, with one of i

Q: JEE Main 2021 Conic Sections: The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8x, with one of i...

The correct answer is A. Here's an elaborate, clear, and educational solution to the problem, designed for a JEE student. --- **1. Understanding the Parabola and its Vertex** The given equation of the parabola is . **Why this step is important:** We need to identify the key features of the parabola to correctly place the triangle. * This equation is in the standard form . * By comparing with , we find , which implies . * The **vertex** of this parabola is at the origin, . * The

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The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8x, with one of its vertices on the vertex of this parabola, is :

Accepted Answer

Here's an elaborate, clear, and educational solution to the problem, designed for a JEE student.

1. Understanding the Parabola and its Vertex

The given equation of the parabola is $y^2 = 8x$ . Why this step is important: We need to identify the key features of the parabola to correctly place the triangle.

This equation is in the standard form $y^2 = 4ax$ .
By comparing $y^2 = 8x$ with $y^2 = 4ax$ , we find $4a = 8$ , which implies $a = 2$ .
The vertex of this parabola is at the origin, $A = (0,0)$ .
The

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