Question

The equation of lines passing through $(2,3)$ and making an intercept of length $\sqrt{10}$ between the lines $2x+y-3=0$ and $2x+y-4=0$ are......

• A. $13x+5y-41=0,3x+5y-21=0$
• B. $13x+9y-53=0,3x+y-9=0$
• C. $13x-7y-5=0,3x-3y+6=0$
• D. $9x+13y-57=0,x+3y-11=0$

Answer 1

The correct option is B $13x+9y-53=0,3x+y-9=0$

Distance b/w parallel lines $\left(AL\right)=\frac{1}{\sqrt{5}}$

$\begin{array}{c}LB=\sqrt{10-\frac{1}{5}}=\frac{7}{\sqrt{5}}\\ \tan \alpha =\frac{1}{7}\end{array}$

Slope of lines are $\tan \left(x+\alpha \right)or\tan \left(x-\alpha \right)where\tan x=-2$

$\begin{array}{c}\frac{-2+\frac{1}{7}}{1-\left(-2\right)\frac{1}{7}}=\frac{-2-\frac{1}{7}}{1-2\left(\frac{1}{7}\right)}\\ =\frac{\frac{-13}{7}}{\frac{9}{7}}=\frac{-\frac{15}{7}}{\frac{5}{7}}\\ =\frac{-13}{9}=-3\\ y-3=\frac{-13}{9}\left(x-2\right)ory-3=-\left(x-2\right)\\ 9y-27=-13x+26y+3x-9=0\\ 13x+9y-53=0\end{array}$

Option $B$ is correct answer.