Let PQ be a focal chord of length 6.25 units of the parabola y 2 = 4x. If O is the vertex of the par

Q: JEE Main 2023 Conic Sections: Let PQ be a focal chord of length 6.25 units of the parabola y 2 = 4x. If O is the vertex of the par...

The correct answer is 2. This solution will guide you through calculating the area of a triangle formed by the vertex and the endpoints of a focal chord of a parabola. We will systematically use the properties of parabolas and focal chords to find the necessary parameters and then apply the area formula. --- **1. Key Concept: Area of a Triangle with Vertex at Origin** The fundamental concept we will use is the formula for the area of a triangle when one of its vertices is at the origin. Given three vertices , , and , th

Question

Let PQ be a focal chord of length 6.25 units of the parabola y 2 = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of POQ is equal to .

Accepted Answer

This solution will guide you through calculating the area of a triangle formed by the vertex and the endpoints of a focal chord of a parabola. We will systematically use the properties of parabolas and focal chords to find the necessary parameters and then apply the area formula.

1. Key Concept: Area of a Triangle with Vertex at Origin

The fundamental concept we will use is the formula for the area of a triangle when one of its vertices is at the origin. Given three vertices $O(0,0)$ , $P(x_P, y_P)$ , and $Q(x_Q, y_Q)$ , the area of $\Delta POQ$ is given by:

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