WBJEE · Maths · Properties of Triangles
\(A, B\) are fixed points with coordinates \((0, a)\) and \((0, b)(a > 0, b > 0)\). \(P\) is variable point \((x, 0)\) referred to rectangular axis. If the angle \(\angle \mathrm{APB}\) is maximum, then
- A \(x^2=a b\)
- B \(x^2=a+b\)
- C \(x=\frac{1}{a b}\)
- D \(x=\frac{a+b}{2}\)
Answer & Solution
Correct Answer
(A) \(x^2=a b\)
Step-by-step Solution
Detailed explanation
Hint : \(\angle A P B=\theta=\cos ^1\left(\frac{x^2+a^2+x^2+b^2-(a-b)^2}{2 \sqrt{x^2+a^2} \sqrt{x^2+b^2}}\right)\) For Max; \(\frac{\mathrm{d} \theta}{\mathrm{dx}}=0, \mathrm{x}^2=\mathrm{ab}\)
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