A line with positive rational slope, passes through the point A(6,0) and is at a distance of 5 units from B (1,3). The slope of line is

Options

A. `(15)/(8)`
B. `(8)/(15)`
C. `(5)/(8)`
D. `(8)/(5)`

Answer

B

Explanation

Equation of line through point A(6,0) and having slope m is
`(y-0)=m(x-6),m gt 0`
`"or "mx-y-6m=0, m gt 0 " "...(1)`
Distance of this line from point B(1,3) is 5.
`"So, " |(m-3-6m)/(sqrt(1+m^(2)))|=5`
`rArr (3+5m)^(2)=25(1+m^(2))`
`rArr 9+30m = 25`
`rArr m=(16)/(30) = (8)/(15)`