Q78 / 150 · MHT CET 2017 · Mathematics

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

A
$\frac{y}{x}$
B
$\frac{- x}{y}$
Correct answer
C
$\frac{x}{y}$
D
$\frac{- y}{x}$

Solution

x = a (t - \frac{1}{t}), y = a (t + \frac{1}{t})

y^{2} - x^{2} = a^{2} [{(t + \frac{1}{t})}^{2} - {(t - \frac{1}{t})}^{2}]

y^{2} - x^{2} = 4 a^{2}

Differentiate w.r.t. x

2 y \frac{d y}{d x} - 2 x = 0

∴ \frac{d y}{d x} = \frac{x}{y}

Hence, the correct answer is option: 'C'.

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