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NDA2016MathematicsDifferential EquationsActual

What is the curve which passes through the point (1,1) and whose slope is 2 y x ?

Options

  1. ACircle
  2. BParabola
  3. CEllipse
  4. DHyperbola

Correct answer

B. Parabola

Step-by-step solution

aligned & d y d x = 2 y x & d y y =2 d x x aligned On integration aligned & d y y =2 d x x & y=2 x+ a & y= x^2+ a & y= (x^2 a ) & y=x^2 a & at (1,1) ; a=1 & x^2=y=4 ( 1 4 ) y aligned the curve is parabola.

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