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JEE Main201910 Jan 2019Evening ShiftMathematicsDifferential EquationsActual

A curve amongst the family of curves represented by the differential equation, x 2 - y 2 d x + 2 x y d y = 0 which passes through 1 , 1 , is

Options

  1. AA circle with centre on the x - axis.
  2. BA circle with centre on the y - axis.
  3. CA hyperbola with transverse axis along the x - axis.
  4. DAn ellipse with major axis along the y - axis.

Correct answer

A. A circle with centre on the x - axis.

Step-by-step solution

x 2 d x - y 2 d x + 2 x y   d y = 0 x 2 d x = y 2 d x - 2 x   y d y ⇒ - d x = d y 2 x (exact differential equation) ⇒   - x = y 2 x + C ⇒   x 2 + y 2 + C x = 0 ∵   It passes through 1 , 1 . Hence, C = - 2 ⇒   x 2 + y 2 - 2 x = 0

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