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Latus Rectum of Hyperbola

The latus rec...

Question

The latus rectum of the parabola whose focal chord is PSQ such that SP = 3 and SQ = 2 is

A

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B

6

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C

18

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D

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Solution

The correct option is A

Latus rectum= $\frac{4 S P . S Q}{S p + S Q} \Rightarrow l a t u s r e c t u m = \frac{4.3.2}{3 + 2} = \frac{24}{5}$

$(∵$ semi-latus rectum of a parabola is H.M of segments of a focal chord)

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Similar questions

Q. Find the latus rectum of a parabola whose focal chord

P S Q

S P = 3

S Q = 2.

Q. The latus rectum of a parabola whose focal chord is

P S Q

S P = 3

S Q = 2

P S Q

is the focal chord of a parabola such that

S P = 2

S Q = 4

then the length of the latus rectum is

P S Q

is the focal chord of a parabola such that

S P = 2

S Q = 4

then the length of the latus rectum is

Q. Assertion :If

P S Q

is the focal chord of the parabola

y^{2} = 8 x

S P = 6

, then the length

S Q

3

. Reason: The semi-latus rectum of a parabola is the harmonic mean between the segment of any focal chord of a parabola.

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