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Tangents are drawn from any point on the directrix of y 2 = 16 x to the parabola. If the locus of the midpoint of chords of contact is a parabola, then its length (in units) of the latus rectum is

Correct answer

8

Step-by-step solution

Equation of the chord of contact P Q :   T = S 1 ⇒ y k - 8 x + h = k 2 - 16 h … … . i According to the property, the chord of contact w.r.t. any point on the directrix always passes through focus 4,0 i.e., 4,0 satisfy the equation i ⇒ - 8 4 + h = k 2 - 16 h ⇒ - 32 - 8 x = y 2 - 16 x y 2 = 8 x - 4 ⇒ Length of the latus rectum is 8 units

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