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If the segment between thelines x+6y-13=...

If the segment between thelines `x+6y-13=0` and `x-y+3=0` is bisected at `(6, 8)` then length of segment is :

A

`sqrt(268)`

B

`sqrt(244)`

C

`sqrt(212)`

D

`sqrt(252)`

Text Solution

Verified by Experts

The correct Answer is:
B
If the segment ………….
Let the segment is `AB` as shown in the figure.

Let `A = (13-6y_(1), y_(1))`
`B = (y_(2)-3, y_(2))`
`:'` mid point of `AB = (5, 8)`
`:. (13-6y_(1)+y_(2)-3)/(2) = 6` ....(i)
and `(y_(1)+y_(2))/(2)` .....(ii)
on solving (i) and (ii)
`A = (1,2)`
`B =(11, 14)`
`L_(AB) = sqrt(244)`
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