Question

Let \(\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}\). Then
(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) \(x y_{2}+5 x y_{1}-3 y=0\)

Answer 1

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