If `P(1+t/(sqrt(2)),2+tsqrt(2))` is any point on a line, then the range of the values of `t` for which the point `P` lies between the parallel lines `x+2y=1a n d2x+4y=15.` is `4(sqrt(2))/3

Options

A. `((-4sqrt2)/(5) , (5sqrt2)/(6)) `
B. `(0 , (5sqrt2)/(6))`
C. `((-4sqrt2)/(5) , 0) `
D. none of these

Explanation

If point P lies between the given parallel lines , then
`(1 + (t)/(sqrt2) + 4 + (2t)/(sqrt2) - 1) (2 + (2t)/(sqrt2) + 8 + (4t)/(sqrt2) - 15) lt 0`
`implies (4 + (3t)/(sqrt2)) ( - 5 + (6t)/(sqrt2)) lt 0`
`implies (-4sqrt2)/(3) lt t lt (5sqrt2)/(6) implies t in ((-4 sqrt2)/(5) , (5 sqrt2)/(6))`