The line is the directrix of the ellipse with the corresponding focus . If the tangent to at the poi

Q: JEE Main 2023 Conic Sections: The line is the directrix of the ellipse with the corresponding focus . If the tangent to at the poi...

The correct answer is 8. This problem requires a comprehensive understanding of ellipses, encompassing their definition, standard equation, properties related to foci and directrices, and the equation of a tangent. We will systematically determine the ellipse's parameters, locate the point of tangency, find the x-intercept of the tangent, and finally calculate the required distance. --- **1. Key Concepts and Formulas** Before diving into the calculations, let's recall the fundamental properties of an ellipse centered at

Question

The line is the directrix of the ellipse with the corresponding focus . If the tangent to at the point in the first quadrant passes through the point and intersects the -axis at , then is equal to .

Accepted Answer

This problem requires a comprehensive understanding of ellipses, encompassing their definition, standard equation, properties related to foci and directrices, and the equation of a tangent. We will systematically determine the ellipse's parameters, locate the point of tangency, find the x-intercept of the tangent, and finally calculate the required distance.

1. Key Concepts and Formulas

Before diving into the calculations, let's recall the fundamental properties of an ellipse centered at the origin with its major axis along the x-axis:

Standard Equation: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ , where $a > b > 0$ .
Foci: $(\pm ae,

Question

Solution

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