If x = a t - 1 t , y = a t + 1 t where t be the parameter then d y d x = ?

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Question: Answered & Verified by Expert

If

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

where

t

be the parameter then

\frac{d y}{d x} = ?

MathematicsDifferentiationMHT CETMHT CET 2017

Options:

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

Solution:

1244 Upvotes Verified Answer

The correct answer is:

\frac{x}{y}

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}

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