Differentiation Question 424
Question: If $ x=a( t-\frac{1}{t} ),y=a $
$ ( t+\frac{1}{t} ) $ then $ \frac{dy}{dx}= $
[Karnataka CET 2004]
Options:
A) $ \frac{y}{x} $
B) $ \frac{-y}{x} $
C) $ \frac{x}{y} $
D) $ \frac{-x}{y} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ x=a( t-\frac{1}{t} ) $ ….(i) and $ y=a( t+\frac{1}{t} ) $ …..(ii) Squaring (i) and (ii), then subtracting we get, $ x^{2}-y^{2}=a^{2}(-4) $ or $ y^{2}-x^{2}=4a^{2} $
Differentiating both sides w.r.t. x, $ 2y\frac{dy}{dx}-2x=0 $
Therefore $ \frac{dy}{dx}=\frac{x}{y} $ .
BETA
