If tangents are drawn to the ellipse x2 + 2y 2 = 2 at all points on the ellipse other than its four

Q: JEE Main 2019 Conic Sections: If tangents are drawn to the ellipse x2 + 2y 2 = 2 at all points on the ellipse other than its four ...

The correct answer is A. This problem asks us to find the locus of the midpoints of tangent segments to an ellipse, where these segments are intercepted between the coordinate axes. This is a classic locus problem involving tangents. We will use the parametric form of the ellipse, the equation of a tangent, and the midpoint formula, culminating in the elimination of the parameter to find the desired locus. --- **1. Understanding the Ellipse and its Parametric Form** The first step is to correctly identify the standard f

Question

If tangents are drawn to the ellipse x2 + 2y 2 = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

Accepted Answer

This problem asks us to find the locus of the midpoints of tangent segments to an ellipse, where these segments are intercepted between the coordinate axes. This is a classic locus problem involving tangents. We will use the parametric form of the ellipse, the equation of a tangent, and the midpoint formula, culminating in the elimination of the parameter to find the desired locus.

1. Understanding the Ellipse and its Parametric Form

The first step is to correctly identify the standard form of the given ellipse and express a general point on it using parametric coordinates.

Given Ellipse Equation: $x^2 + 2y^2 = 2$
Standard Form: To get the standard form $\frac{x^2}{a^2} + \frac

Answer

x 2 2 + y 2 4 = 1

Answer

1 2 x 2 + 1 4 y 2 = 1

Answer

1 4 x 2 + 1 2 y 2 = 1

Answer

x 2 4 + y 2 2 = 1

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Solution

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