Question

Equations of lines which pass through the points of intersection of the lines $4x-3y-1=0$ and $2x-5y+3=0$ and are equally inclined to the axes are

• A. $y\pm x=0$
• B. $y–1=\pm 1(x–1)$
• C. $x–1=\pm 2(y–1)$
• D. None of these

Answer 1

The correct option is B

$y–1=\pm 1(x–1)$

Step 1. Find the point of intersection:

$4x–3y–1=0$ …..(i)

$2x–5y+3=0$ …..(ii)

By solving equation (i) and (ii), we get,

$x=1,y=1$

$\therefore$The point of intersection is $(1,1)$

Also, the Required lines are to be equally inclined to the axes.

Thus, there will be two lines passing through $(1,1)$ which are equally inclined to the axes with the angle $\theta =45°$ and $135°$

Step 2. Find the equation of the line:

So the slope $m$ of the line will be,

$\tan \theta =\left(\tan 45°,\tan 135°\right)$

$=\pm 1$

$\therefore$The required equation of the line is

$y–y_1=m(x–x_1)$

$\Rightarrow$$\mathit{y}\mathbf{}\mathbf{–}\mathbf{}\mathbf{1}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\pm }\mathbf{1}\mathbf{(}\mathit{x}\mathbf{}\mathbf{–}\mathbf{}\mathbf{1}\mathbf{)}$

Hence, Option ‘B’ is Correct.