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Question

The latus rectum of the parabolay2=4ax, whose focal chord is PSQ, such that SP=3 and SQ=2 are given by


A

245

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B

125

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C

65

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D

15

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Solution

The correct option is A

245


Explanation for the correct option:

Latus-rectum and semi length of focal chord:

A chord through the focus of the parabola parallel to the directrix of the parabola is called the latus rectum of the parabola

The half of the length of this chord is called semi latus rectum

The semi latus rectum is a harmonic mean between the two segments of a focal chord

Let l be the length of the semi latus rectum of the parabola

We know,

2l=1SP+1SQ

⇒2l=13+12=56

⇒ l=125

⇒ 2l=245

The length of the latus rectum =245.

Hence, option A is correct.


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