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NDA 2019 Maths · Mathematics · Differential Equations · easy

The curve satisfying dy/dx=-x/y and passing through the point (0,3) is

Single correct option

The curve satisfying dydx=−xy\dfrac{dy}{dx}=-\dfrac xy and passing through the point (0,3)(0,3) is
  1. A. x2+y2=9x^2+y^2=9
  2. B. x2−y2=−9x^2-y^2=-9
  3. C. y=3−xy=3-x
  4. D. x2+y2=3x^2+y^2=3
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Answer: (A) x2+y2=9x^2+y^2=9

Separate variables: y dy=−x dxy\,dy=-x\,dx, so y22=−x22+C\frac{y^2}{2}=-\frac{x^2}{2}+C, i.e. x2+y2=cx^2+y^2=c. At (0,3)(0,3), c=9c=9. The sign matters: a minus sign in dydx\frac{dy}{dx} gives circles, while +xy+\frac xy would give hyperbolas. x2+y2=3x^2+y^2=3 forgets to square the 33.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake