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A chord is drawn through the focus of the parabola y ⁡ 2 = 6 x ⁡ such that its distance from the vertex of this parabola is 5 2 , then its slope can be

Options

  1. A5 2
  2. B2 3
  3. C3 2
  4. D2 5

Correct answer

A. 5 2

Step-by-step solution

The focus and vertex of a parabola y 2 = 4 a x are respectively a ,   0 and 0 ,   0 . The given parabola is y 2 = 6 x   ⇒ a = 3 2 Thus, the focus and vertex are respectively S ≡ 3 2 ,   0 and V ≡ 0 ,   0 . The equation of a line passing through a point x 1 ,   y 1 and having slope m is y - y 1 = m x - x 1 If m is the slope of the chord through focus 3 2 ,   0 , equation of the chord is y - 0 = m x - 3 2 ⇒ 2 m x -2 y -3 m =0 We know that the length of perpen

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