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AP EAMCET20224 Jul 2022Morning ShiftMathematicsParabolaActual

If a x + b y = 1 is a normal to the parabola y 2 = 4 p x then the condition is

Options

  1. A4 a b = a 2 + b 2
  2. B4 p a b + a b 3 = a 2 b 2
  3. Cp a 3 = b 2 - 2 p a b 2
  4. Dp a 2 + 1 p a = a + b

Correct answer

C. p a 3 = b 2 - 2 p a b 2

Step-by-step solution

For the parabola y 2 = 4 p x , the equation of normal is y = m x - 2 p m - p m 3 . Comparing it with the given equation of normal y = - a b x + 1 b , we get - a b = m ;   - 2 p m - p m 3 = 1 b i.e. - 2 p - a b - p - a b 3 = 1 b ⇒ 2 p a b + p a 3 b 3 = 1 b ⇒ 2 p a b 2 + p a 3 = b 2

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