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$A (a, 0) B (- a, 0)$ are two points. If a point P moves such that $P A B - P B A = 2 α$ then the locus of P is

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$x^{2} + 2 x y \tan 2 α - y^{2} = a^{2}$

$x^{2} + 2 x y \cot α + y^{2} = a^{2}$

$x^{2} - 2 x y \tan^{2} 2 α + y^{2} = a^{2}$

$x^{2} + 2 x y \cot 2 α - y^{2} = a^{2}$

answer is D.

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Detailed Solution

$\tan β = \frac{y}{a - x}$

$\tan γ = \frac{y}{a + x}$

$\tan 2 α = \tan (β - γ)$

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