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JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Mathematics
Chapter
Differential Equations

JEE Advanced 2007 · Paper 2 · Mathematics · Differential Equations

The differential equation (d y)/(d x)= 1-y^2 y determines a family...

The differential equation dydx=1−y2y\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y} determines a family of circles with

Options

  1. Avariable radii and a fixed centre at (0,1)(0,1)
  2. Bvariable radii and a fixed centre at (0,−1)(0,-1)
  3. Cfixed radius 1 and variable centres along the X\mathrm{X}-axis
  4. Dfixed radius 1 and variable centres along the Y\mathrm{Y}-axis

Correct answer

C. fixed radius 1 and variable centres along the X\mathrm{X}-axis

Step-by-step solution

dydx=1−y2y⇒∫y1−y2dy=\intdx⇒−1−y2=x+C⇒(x+c)2+y2=1\begin{aligned}& \frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}\\ & \Rightarrow \quad \int \frac{y}{\sqrt{1-y^2}}d y=\intd x \\ & \Rightarrow \quad-\sqrt{1-y^2}=x+C \\ & \Rightarrow \quad(x+c)^2+y²=1 \\ & \end{aligned}Centre (−C,0)(-C, 0) and radius =1=1.
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