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JEE Main20208 Jan 2020Evening ShiftMathematicsApplication of DerivativesActual

The length of the perpendicular from the origin, on normal to the curve, x 2 + 2 x y - 3 y 2 = 0 , at the point 2 ,   2 , is.

Options

  1. A2
  2. B4 2
  3. C2
  4. D2 2

Correct answer

D. 2 2

Step-by-step solution

x 2 + 2 x y - 3 y 2 = 0 Differentiate the above curve, 2 x + 2 x y ' + y - 6 y y ' = 0 So, at 2 ,   2 ,   y ' = 1 . So, equation of normal to the curve at 2 ,   2 is x + y = 4 . Thus, perpendicular distance from origin on the normal is 0 + 0 - 4 1 2 + 1 2 = 4 2 = 2 2 .

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