Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4

Q: JEE Main 2023 Conic Sections: Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 ...

The correct answer is C. **Key Concepts and Formulas:** 1. **Standard Equation of a Parabola:** For a parabola with vertex and its axis of symmetry parallel to the x-axis, its equation is given by . * The focus of this parabola is at . * The parameter ' ' represents the directed distance from the vertex to the focus. If , the parabola opens to the right; if , it opens to the left. * The directrix of this parabola is the line . 2. **Chord of Contact:** If tangents are drawn from an external point $

Question

Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O(0, 0) to the parabola P which meet P at S and R, then the area (in sq. units) of SOR is equal to :

Accepted Answer

**Key Concepts and Formulas:** 1. **Standard Equation of a Parabola:** For a parabola with vertex and its axis of symmetry parallel to the x-axis, its equation is given by . * The focus of this parabola is at . * The parameter ' ' represents the directed distance from the vertex to the focus. If , the parabola opens to the right; if , it opens to the left. * The directrix of this parabola is the line . 2. **Chord of Contact:** If tangents are drawn from an external point $

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16

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32

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