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JEE Main20198 Apr 2019Morning ShiftMathematicsEllipseActual

If the tangents on the ellipse 4 x 2 + y 2 = 8 at the points 1, 2 and ( a , b ) are perpendicular to each other, then a 2 is equal to

Options

  1. A2 17
  2. B4 17
  3. C64 17
  4. D128 17

Correct answer

A. 2 17

Step-by-step solution

4 x 2 + y 2 = 8 ⇒ 8 x + 2 y d y d x = 0 d y d x = - 8 x 2 y = - 4 x y ∴ Slope at 1 ,   2 ,   m 1 = - 2 Slope at a , b ,   m 2 = - 4 a b ∴ - 2 × - 4 a b = - 1 b = - 8 a Again, 4 a 2 + b 2 = 8 ⇒ 4 a 2 + 64 a 2 = 8 ⇒ 68 a 2 = 8 ⇒ a 2 = 8 68 ⇒ a 2 = 2 17

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