Question

The equation of straight lines passing through points $(2,3)$ and having an intercept of length $2$ units between the straight lines $2x+y=3,2x+y=5$.

• A. $3x+4y=18$
• B. $3x+4y=12$
• C. $x-2=0$
• D. $x+2=0$

Answer 1

Answer: (A), (C)

The correct options are
A $3x+4y=18$
C $x-2=0$

Let m be the slope of the required line.
Equation of lines having slope m and passing through $(2,3)$ is
$y-3=m(x-2)$ .....(i)
Given lines $2x+y=3$ .....(ii)
and $2x+y=5$ .....(iii)
Point of intersection of (i) and (ii) is $(\frac{2m}{2+m},\frac{6-m}{2+m})$
Point of intersection of (ii) and (iii) is $(\frac{2m+2}{2+m},\frac{6+m}{2+m})$
Since, the required lines have an intercept of 2 units.
$\Rightarrow (\frac{2m}{2+m}-\frac{2m+2}{2+m}{)}^2+(\frac{6-m}{2+m}-\frac{6+m}{2+m}{)}^2=4$
$\Rightarrow m=-\frac{3}{4}$, $m=0$
So, the equation of required line is
$3x+4y=18$