Let , be a conic. Let S be the focus and B be the point on the axis of the conic such that , where A

Q: JEE Main 2024 Conic Sections: Let , be a conic. Let S be the focus and B be the point on the axis of the conic such that , where A...

The correct answer is A. This problem combines concepts from conic sections (specifically parabolas), coordinate geometry (focus, axis, perpendicularity, centroid), and limits. We will systematically break down the problem to find the coordinates of the involved points, calculate the centroid, and then evaluate the limit. **1. Identifying the Conic and its Key Properties** The conic is given by the parametric equations: Our first step is to convert these parametric equations into a standard Cartesian form to identify th

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Let , be a conic. Let S be the focus and B be the point on the axis of the conic such that , where A is any point on the conic. If k is the ordinate of the centroid of the SAB, then is equal to :

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This problem combines concepts from conic sections (specifically parabolas), coordinate geometry (focus, axis, perpendicularity, centroid), and limits. We will systematically break down the problem to find the coordinates of the involved points, calculate the centroid, and then evaluate the limit.

1. Identifying the Conic and its Key Properties

The conic is given by the parametric equations: $x = 2t \quad \text{and} \quad y = \frac{t^2}{3}$

Our first step is to convert these parametric equations into a standard Cartesian form to identify the type of conic and its key properties like the focus and axis.

From the first equation, we can express $t$ in terms of $x$ : $t = \frac{x}{2}$ .

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