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Consider a parabola whose axis is along $x -$ axis and which touches the pair of lines $x 2 − y 2 − 2 x + 1 = 0$ and having focus at $(5, 0)$ . If $P Q ¯$ is a focal chord of that parabola, the harmonic mean of segments of that focal chord of parabola is

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12

14

answer is D.

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Detailed Solution

Clearly given pair of lines are

⊥ r

lines, intersecting at (1, 0) so, (1, 0) lies on directrix of parabola as well as axis of parabola. So, it is z in usual notation.

∴ S Z ¯ = 4

ie semi-latusrectum = 4

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