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Slope of the chord of parabola y 2 = 4 a x which passes through the point - 6 a ,   0 and which subtends an angle of 45 ° at the vertex, is

Options

  1. A± 2 7
  2. B± 3 8
  3. C± 7 2
  4. D± 5 6

Correct answer

A. ± 2 7

Step-by-step solution

Given parabola y 2 = 4 a x . Focus lies at a ,   0 and vertex lies at 0 ,   0 . Now, equation of chord passing through given point is y = m ( x + 6 a ) ⇒ y - m x 6 a m = 1 Homogenizing it with the parabola, y 2 - 4 a x y - m x 6 a m = 0 ⇒ 4 a m x 2 + 6 a m y 2 - 4 a x y = 0 It is given that chord subtends 45 ° angle at origin. Therefore, tan ⁡ 45 o = 2 4 a 2 - 24 a 2 m 2 4 a m + 6 a m ⇒ 100 a 2 m 2 = 4 4 a 2 - 24 a 2 m 2 ⇒ 49 m 2 = 4 ⇒ m = ± 2 7

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