Let ABCD be a trapezium whose vertices lie on the parabola . Let the sides AD and BC of the trapeziu

Q: JEE Main 2023 Conic Sections: Let ABCD be a trapezium whose vertices lie on the parabola . Let the sides AD and BC of the trapeziu...

The correct answer is A. This problem involves finding the area of a trapezium whose vertices lie on a parabola, utilizing properties of focal chords and geometric formulas. --- **1. Understanding the Parabola and Parametric Representation** The given parabola is . This is of the standard form , where . The focus of this parabola is at , which is . Any point on the parabola can be represented parametrically as for some real parameter . This representation is extremely useful for calculations involving points on the para

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Let ABCD be a trapezium whose vertices lie on the parabola . Let the sides AD and BC of the trapezium be parallel to -axis. If the diagonal AC is of length and it passes through the point , then the area of is

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This problem involves finding the area of a trapezium whose vertices lie on a parabola, utilizing properties of focal chords and geometric formulas.

1. Understanding the Parabola and Parametric Representation

The given parabola is $y^2 = 4x$ . This is of the standard form $y^2 = 4ax$ , where $a=1$ . The focus of this parabola is at $(a,0)$ , which is $(1,0)$ .

Any point on the parabola $y^2 = 4x$ can be represented parametrically as $P(t) = (t^2, 2t)$ for some real parameter $t$ . This representation is extremely useful for calculations involving points on the parabola.

**2. Defining the Vertices of the Trapezium

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