Question

If $x = a (t - \frac { 1}{t}) , y = a ( t + \frac {1}{t})$ where $t$ be the parameter then $\frac{dy}{dx} = ? $

• A. $\frac{y}{x} $
• B. $\frac{- x}{y} $
• C. $\frac{x}{y} $
• D. $\frac{ - y}{x} $

Answer 1

Answer: (C)

$x=a\left(t-\frac{1}{t}\right), y=a\left(t+\frac{1}{t}\right) $
$y^{2}-x^{2}=a^{2}\left[\left(t+\frac{1}{t}\right)^{2}-\left(t-\frac{1}{t}\right)^{2}\right] $
$y^{2}-x^{2}=4 a^{2}$
Differentiate w.r.t.$x$
$2 y \frac{d y}{d x}-2 x=0$
$\therefore \frac{d y}{d x}=\frac{x}{y}$