Question

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

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

Answer 1

The correct option is A $3x+4y=18$

Let the line equation be $ax+by=c$ and the condition that $(2,3)$ lies on the line $2a+3b=c$ and the intercept between the lines $2x+y=k;k_1=3,k_2=5$ is $2^2=(\frac{k_{1}b-k_{2}b}{2b-a}{)}^2+(\frac{a{k}_2-a{k}_1}{2b-a}{)}^2⟹(2b-a{)}^2=a^2+b^2⟹3b=4a$

$c=2a+4a=6a⟹ax+\frac{4a}{3}y=6a⟹3x+4y=18$