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MHT CET20228 Aug 2022Evening ShiftMathematicsDifferential EquationsActual

The equation of the curve passing through the point (0,-2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y -co-ordinate of the point is equal to the x -co-ordinate of the point, is

Options

  1. Ay^2+x^2=4
  2. By^2-x^2=4
  3. C2 y^2+x^2=8
  4. D4 y^2+3 x^2=16

Correct answer

B. y^2-x^2=4

Step-by-step solution

aligned & A / Q d y d x y=x & y d y= x d x & y^2 2 = x^2 2 +c aligned putting x=0 and y=-2 we get c=2 aligned & y^2 2 = x^2 2 +2 & y^2-x^2=4 aligned

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