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GATE 2019 EC – Question 12

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

The families of curves represented by the solution of the equation

$$\frac{dy}{dx}=-\left(\frac xy\right)^n$$

for $n=-1$ and $n=+1$, respectively, are

  1. Parabolas and Circles
  2. Circles and Hyperbolas
  3. Hyperbolas and Circles
  4. Hyperbolas and Parabolas

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Show answer and explanation

Correct answer: (C) Hyperbolas and Circles

Explanation

For $n=-1$, $\frac{dy}{dx}=-\frac yx$ gives $xy=c$, a family of hyperbolas. For $n=1$, $y\,dy=-x\,dx$ gives $x^2+y^2=c$, a family of circles.