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The chord A B of the parabola y^2=4a x c...

The chord `A B` of the parabola `y^2=4a x` cuts the axis of the parabola at `Cdot` If `A-=(a t1 2,2a t_1),B-=(a t2 2,2a t_2)` , and `A C : A B1:3,` then prove that `t_2+2t_1=0` .

A

`t_(2)=2t_(1)`

B

`t_(2) +2t_(1) =0`

C

`t_(1)+2t_(2)=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`A("at"_(1)^(2), 2"at"_(1)) " and " B("at"_(2)^(2), 2"at"_(2))` are such that
`AC : AB 1:3`
`:. C((2"at"_(1)^(2)+"at"_(2)^(2))/(3),(4"at"_(1)+2"at"_(2))/(3))`
Point C lines on x- axis then
`(4"at"_(1)+2"at"_(2))/(3) =0`
`rArr t_(2) +2t_(1)=0`
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