Let a line L 1 be tangent to the hyperbola and let L 2 be the line passing through the origin and pe

Q: JEE Main 2021 Conic Sections: Let a line L 1 be tangent to the hyperbola and let L 2 be the line passing through the origin and pe...

The correct answer is 1. This problem asks us to find the locus of the point of intersection of a tangent to a hyperbola and a line passing through the origin perpendicular to that tangent. This specific type of locus is known as the pedal curve of the hyperbola with respect to the origin. We will derive this locus using the general equation of a tangent to a hyperbola in slope form. --- **1. Key Concept: Equation of a Tangent to a Hyperbola in Slope Form** For a standard hyperbola given by the equation , the equation o

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Let a line L 1 be tangent to the hyperbola and let L 2 be the line passing through the origin and perpendicular to L 1 . If the locus of the point of intersection of L 1 and L 2 is , then + is equal to .

Accepted Answer

This problem asks us to find the locus of the point of intersection of a tangent to a hyperbola and a line passing through the origin perpendicular to that tangent. This specific type of locus is known as the pedal curve of the hyperbola with respect to the origin. We will derive this locus using the general equation of a tangent to a hyperbola in slope form.

1. Key Concept: Equation of a Tangent to a Hyperbola in Slope Form

For a standard hyperbola given by the equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ , the equation of a tangent line with slope $m$ is:

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