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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Differentiation

NDA 2015 · Mathematics · Differentiation

Consider the parametric equation x=(a(1-t^2))/(1+t^2), y=(2 a...

Consider the parametric equation x=a(1−t2)1+t2,y=2at1+t2x=\frac{a\left(1-t^2\right)}{1+t^2}, y=\frac{2 a t}{1+t^2} What is dydx\frac{d y}{d x} equal to?

Options

  1. Ayx\frac{y}{x}
  2. B−yx-\frac{y}{x}
  3. Cxy\frac{x}{y}
  4. D−xy-\frac{x}{y}

Correct answer

D. −xy-\frac{x}{y}

Step-by-step solution

Here, x2+y2=a2∴2x+2ydydx=0∴dydx=2x−2y=−xy∴x^2+y^2=a^2\therefore \quad 2 x+2 y \frac{d y}{d x}=0\therefore \quad \frac{d y}{d x}=\frac{2 x}{-2 y}=-\frac{x}{y}\therefore \quad Option (D) is correct.
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