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The line L given by x/5 + y/b = 1 passes...

The line L given by `x/5 + y/b = 1` passes through the point (13,32).the line K is parallel to L and has the equation `x/c+y/3=1` then the distance between L and K is

A

`(23)/(sqrt(17))`

B

`(23)/(sqrt(15))`

C

`sqrt(17)`

D

`(17)/(sqrt(15))`

Text Solution

Verified by Experts

The slope of line L is -b/5.
The slope of line K is -3/c.
The line L is parallel to the line K. Therefore,
`(b)/(5) = (3)/(c) rArr bc = 15`
(13, 32) is a point on L. So
`(13)/(5) + (32)/(b) =1`
`rArr (32)/(b) =-(8)/(5) rArr b = -20`
`therefore c = -(3)/(4)`
The equation of K is y-4x= 3.
Hence, the distance between L and K
= distance of point (13, 32) from line K
`=(|52-32+3|)/(sqrt(17)) = (23)/(sqrt(17))`
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