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A $(0, a)$ , B $(0, b)$ be fixed points. $P (x, 0)$ a variable point. The angle $∠ A P B$ is maximum if

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$x^{2} = a b$

$x = b a$

$x^{2} = 2 a b$

$2 x^{2} = a b$

answer is A.

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Detailed Solution

$\cos θ = \frac{P A^{2} + P B^{2} - A B^{2}}{2 P A P B} = \frac{x^{2} + a b}{\sqrt{(x^{2} + a^{2}) (x^{2} + b^{2})}}$ ;

Applying $\frac{d θ}{d x} = 0 \Rightarrow x^{2} = a b$

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