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KCET2019MathematicsApplication of Derivatives

The equation of the curve passing through the point ( (1,1) ) such that the slope of the tangent at any point ( (x, y) ) is equal to the product of its co-ordinates is

Options

  1. A( 2 y=x²+1 )
  2. B( 2 x=y²+1 )
  3. C( 2 x=y²-1 )
  4. D( 2 y=x²-1 )

Correct answer

D. ( 2 y=x²-1 )

Step-by-step solution

d y d x =x y 1 y d y=x d x Integrate y= x² 2 +C (1) Equation (1) passing through (1,1) (1)= 1² 2 +C0= 1 2 +CC=- 1 2 y= ² 2 - 1 2 2 y= ²-1

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