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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Differential Equations

NDA 2015 · Mathematics · Differential Equations

The differential equation of the family of circles passing through...

The differential equation of the family of circles passing through the origin and having centres on the x -axis is

Options

  1. A2xydydx=x2−y22 x y \frac{d y}{d x}=x^2-y^2
  2. B2xydydx=y2−x22 x y \frac{d y}{d x}=y^2-x^2
  3. C2xydydx=x2+y2\quad 2 x y \frac{d y}{d x}=x^2+y^2
  4. D2xydydx+x2+y2=02 x y \frac{d y}{d x}+x^2+y^2=0

Correct answer

B. 2xydydx=y2−x22 x y \frac{d y}{d x}=y^2-x^2

Step-by-step solution

Eq. of family of circles passing through the origin \& having centres on the x -axis is: x2+y2+2gx=02x+2y⋅dydx+2g=0⇒g=−[x+ydydx]\begin{aligned} & x^2+y^2+2 g x=0 \\ & 2 x+2 y \cdot \frac{d y}{d x}+2 g=0 \\ & \Rightarrow g=-\left[x+y \frac{d y}{d x}\right] \end{aligned} [on differentiating] Putting the value of (g) in eq. (1) we get; 2xydydx=y2−x22 x y \frac{d y}{d x}=y^2-x^2
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