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Let A, B and C be three points taken on the parabola `y^(2)=4ax` with coordinates`(at_(i)^(2), 2at_(i)), i=1, 2, 3,` where `t_(1), t_(2)" and "t_(3)` are in A.P. If AA', BB' and CC' are focal chords and coordinates of A', B' and C' are `(at'_(i)^(2), 2at'_(i)),i=1, 2, 3,` them `t'_(1), t'_(2)and t'_(3)` are in

A

AP

B

GP

C

HP

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
It is given AA', BB' and CC' are focal chords.
`:." "t_(1)'=-1/t_(1)," "i=1,2,3.`
`rArr" "t'_(1),t'_(2),t'_(3)" are in H.P. "[becauset_(1),t_(2),t_(3)" are in A.P."]`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Section I - Solved Mcqs
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  16. the shortest distance between the line y-x=1 and the curve x=y^(2) ...

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  17. about to only mathematics

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  18. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

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  19. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

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