Find The Locus Of The Poles Of Tangents To with Respect To The Concentric Ellipse .

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Question

Find the locus of the poles of tangents to with respect to the concentric ellipse .

medium

Solution

Correct option is

The ellipse are

Let (x₁, y₁) be the pole of a tangent (i) with respect to (ii).

Then the polar of (x₁, y₁) with respect to (ii) is

If (iii) touches (i), then

∴ The required locus of (x₁, y₁) is

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