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JEE Main201815 Apr 2018Morning ShiftMathematicsEllipseActual

If is one of the angles between the normals to the ellipse, x^2+3 y^2=9 at the points (3 , 3 ) and (-3 , 3 ) ; (0, 2 ) ; then 2 2 is equal to

Options

  1. A2
  2. B2 3
  3. C1 3
  4. D3 4

Correct answer

B. 2 3

Step-by-step solution

Since, x^2+3 y^2=9 aligned & 2 x+6 y d y d x =0 & d y d x = -x 3 y aligned Slope of normal is - d x d y = 3 y x gathered (- d y d x )(3 , 3 ) = 3 3 3 = 3 =m_ l & (- d x d y )(-3 , 3 ) = 3 3 -3 =- 3 =m₂ gathered As, is the anagle between the normals to the given ellipse then aligned & = | m₁-m₂ 1+m₁ m₂ | &= | 3 + 3 1-3 | &= | 3 + 3 1-3 | aligned So, = 3 2 | + | aligned & 1 = 3 2 | + | & 1 = 3 2 | 1 | & 1 = 3 2 2 2 = 2 3 aligned

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