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The locus of the middle points of the chords of the parabola y 2 = 4 a x , which passes through the origin is

Options

  1. Ay 2 = a x
  2. By 2 = 2 a x
  3. Cy 2 = 4 a x
  4. Dx 2 = 4 a y

Correct answer

B. y 2 = 2 a x

Step-by-step solution

Let mid point be ( x 1 , y 1 ) ∴ Equation of chord is T = S 1 y y 1 - 2 a x + x 1 = y 1 2 - 4 a x 1 Since, it passes through origin ∴ - 2 a x 1 = y 1 2 - 4 a x 1 ⇒ y 1 2 = 2 a x 1 ∴ Locus is y 2 = 2 a x

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