Question

If (x, y) be a variable point on the line $y=2x$ lying between the lines $2(x+1)+y=0$ and $x+3(y-1)=0$ then

• A. $x\in (-\frac{1}{2},\frac{6}{7})$
• B. $x\in (-\frac{1}{2},\frac{3}{7})$
• C. $y\in (-1,\frac{3}{7})$
• D. $y\in (-1,\frac{6}{7})$

Answer 1

Answer: (B), (D)

$y\in (-1,\frac{6}{7})$
$x\in (-\frac{1}{2},\frac{3}{7})$

Given : Point $P(x,y)$ lie on

$y=2x$----(1)

and between the line

$2(x+1)+y=0$

$2x+y+2=0$ and line $x+3(y-1)=0$

$x+3y-3=0$

So

by position of point w.r. to line concept

$2x+y+2>0$

from eq (1)

$2x+2x>-2$

$x>-\frac{1}{2}$

and $x+3y-3<0$

from eq (1)

$7x<3$

$x<\frac{3}{7}$

So $xϵ(-\frac{1}{2},\frac{3}{7})$

and from eq (1)

$\Rightarrow y=2xϵ2(-\frac{1}{2},\frac{3}{7})$

$yϵ(-1,\frac{6}{7})$