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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

A curve passing through the point 1 , 2 and satisfying the condition that slope of the normal at any point is equal to the ratio of ordinate and abscissa of that point, then the curve also passes through the point

Options

  1. A0 , 0
  2. B2 , 2
  3. C2 , 1
  4. D3 , 2

Correct answer

C. 2 , 1

Step-by-step solution

Given - 1 d y d x = y x d y d x = - x y y d y + x d x = 0 y 2 + x 2 = C Since, it passes through 1,2 ⇒ 4 + 1 = C ⇒ C = 5 x 2 + y 2 = 5 Also, passes through 2,1

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