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99 Percentile Qs Bank for JEE MainMathematicsDifferential Equations

At any point x , y on a curve if the length of the subnormal is x - 1 and the curve passes through 1 , 2 then the curve is a conic. A vertex of the curve is

Options

  1. A1 , 0
  2. B0 , 1
  3. C5 , 0
  4. D1 , 2

Correct answer

D. 1 , 2

Step-by-step solution

Let the curve be y = f x Length of subnormal is given by y d y d x i.e. y d y d x = x - 1 On integrating, we get y 2 2 = x 2 2 - x + C Given, the curve passes through 1 , 2 i.e. C = 5 2 So, y 2 = x 2 - 2 x + 5 or y 2 4 - x - 1 2 4 = 1 is an equation of a hyperbola. Its vertex would lie on 1 , ± 2

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