Question

If $P(\frac{1+t}{\sqrt{2}},\frac{2+t}{\sqrt{2}})$ be any point on a line, then the range of values of t for which the point P lies between the parallel lines x + 2y = 1 and 2x + 4y = 15, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let P be on x + 2y = 1
$\Rightarrow 1+\frac{t}{\sqrt{2}}+2(2+\frac{t}{\sqrt{2}})=1$
$\Rightarrow t=-\frac{4\sqrt{2}}{3}$
Let P be on 2x + 3y = 15
$\Rightarrow 2(1+\frac{t}{\sqrt{2}})+4(2+\frac{t}{\sqrt{2}})=15\Rightarrow t=\frac{5\sqrt{2}}{6}$
$\therefore \frac{-4\sqrt{2}}{3}<t<\frac{5\sqrt{2}}{6}$