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

Question

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, $\mathrm{A}=2, \mathrm{~B}=\mathrm{x}^2, \mathrm{C}=\mathrm{n}$, $A=x^2, B=x, C=n^2$, $A=x, B=2 x, C=3 n+1$, $A=x^2, B=3 x, C=2 n$

MARKS App · Accepted Answer

$\begin{aligned} & \text { Hint: } \frac{-1}{\sqrt{1-\frac{y^2}{b^2}}} \times \frac{1}{b} y_1=\left(\frac{n}{n \times \frac{x}{n}}\right) \ & \Rightarrow \frac{-1 y_1}{\sqrt{b^2-y^2}}=\frac{n}{x} \ & \Rightarrow y_1 x+n \sqrt{b^2-y^2}=0 \ & \Rightarrow y_1+x y_2+\frac{n}{2 \sqrt{b^2-y^2}} \cdot(-2 y) y_1=0 \end{aligned}$ $\begin{aligned} & \Rightarrow y_1+x y_2+\frac{n^2}{x} y=0 \ & \Rightarrow y_1 x+x^2 y_2+n^2 y=0 \ & \Rightarrow x^2 y_2+x y_1+n^2 y=0 \ & A=x^2, B=x, C=n^2\end{aligned}$

Search any question & find its solution

Looking for more such questions to practice?