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)/(c) = 1`. Then the distance between L and K is

Options

A. `17//sqrt(15)`
B. `23//sqrt(17)`
C. `23//sqrt(15)`
D. `sqrt(17)`

Answer

B

Explanation

Let `m_(1)` and `m_(2)` be the slopes of lines L and K respectively. Then, `m_(1)=-(b)/(5) and m_(2)=-(3)/(c)`
It is given that the lines L and K are parallel.
`m_(1)=m_(2)`
`implies -(b)/(5)=-(3)/(c)implies bc=15`
Line L passes through the point (13, 32).
`therefore (13)/(5)=(32)/(b)=1implies b=-20`
`therefore ` bc =15 `implies c=-(3)/(4)`
Hence , the equations of lines L and K are `4x-y-20=0` and `4x-y+3=0`
`therefore ` Distance between L and K `=(23)/(sqrt(16+1))=(23)/(sqrt(17))`