Find The Locus Of The Poles Of Normal Chords Of The Hyperbola

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Question

Find the locus of the poles of normal chords of the hyperbola

diffcult

Solution

Correct option is

Let (x₁, y₁) be the pole of a normal chord

of the hyperbola

then (i) must be identical with the polar of (x₁, y₁) with respect to

Comparing (i) and (iii), we obtained

∴ The required locus of (x₁, y₁) is

.

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