WBJEE · Maths · Differentiation
Let \(\cos ^{-1}\left(\frac{y}{b}\right)=\log _e\left(\frac{x}{n}\right)^n\), then \(A y_2+B y_1+C y=0\) is possible for
- A \(\mathrm{A}=2, \mathrm{~B}=\mathrm{x}^2, \mathrm{C}=\mathrm{n}\)
- B \(A=x^2, B=x, C=n^2\)
- C \(A=x, B=2 x, C=3 n+1\)
- D \(A=x^2, B=3 x, C=2 n\)
Answer & Solution
Correct Answer
(B) \(A=x^2, B=x, C=n^2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hint: } \frac{-1}{\sqrt{1-\frac{y^2}{b^2}}} \times \frac{1}{b} y_1=\left(\frac{n}{n \times \frac{x}{n}}\right) \\ & \Rightarrow \frac{-1 y_1}{\sqrt{b^2-y^2}}=\frac{n}{x} \\ & \Rightarrow y_1 x+n \sqrt{b^2-y^2}=0 \\ & \Rightarrow y_1+x y_2+\frac{n}{2…
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