Q41 / 155 · WBJEE 2020 · Mathematics

Let $\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}$. Then

  • Correct answer
    A
    $x^{2} y_{2}+x y_{1}+n^{2} y=0$
  • B
    $x y_{2}-x y_{1}+2 n^{2} y=0$
  • C
    $x^{2} y_{2}+3 x y_{1}-n^{2} y=0$
  • D
    $x y_{2}+5 x y_{1}-3 y=0$

Solution

Hint: $\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}=n \times \log \left(\frac{x}{n}\right)$ $\Rightarrow-\frac{1}{\sqrt{b^{2}-y^{2}}} \cdot y_{1}=\frac{n}{x}$ $\Rightarrow x^{2} y_{1}^{2}=n^{2}\left(b^{2}-y^{2}\right) \Rightarrow x^{2} y_{2}+x y_{1}+n^{2} y=0$

Hence, the correct answer is option: 'A'.

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