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Question: Answered & Verified by Expert
Let $\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}$. Then
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Options:
  • 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:
1774 Upvotes Verified Answer
The correct answer is: $x^{2} y_{2}+x y_{1}+n^{2} y=0$
Hint:
$\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}=n \times \log \left(\frac{x}{n}\right)$
$\Rightarrow-\frac{1}{\sqrt{b^{2}-y^{2}}} \cdot y_{1}=\frac{n}{x}$
$\Rightarrow x^{2} y_{1}^{2}=n^{2}\left(b^{2}-y^{2}\right) \Rightarrow x^{2} y_{2}+x y_{1}+n^{2} y=0$

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