Find the equation of the lines which pass through the point of intersection of the line $4 x - 3 y - 1 = 0$ , $2 x - 5 y + 3 = 0$ and are equally inclined to the axes

Open in App

Solution

By $8 (4) P .5$ , the slope of the line equally inclined to axes is $tan (\pm 45^{o}) = \pm 1$ . Hence by $P + λ Q = 0$ ,
$\frac{2 λ + 4}{5 λ + 3} = \pm 1$
$\Rightarrow λ = \frac{1}{3}, - 1$ . Putting for $λ$ , the two lines are
$x - y = 0, x + y - 2 = 0$ .

Suggest Corrections

Similar questions

Q. The equation of the line(s) passing through the intersection of the lines

4 x - 3 y - 1 = 0

and

2 x - 5 y + 3 = 0

and equally inclined to the axis is/are

Find the equation of the stright line passing through the point of intersection of $2 x + 3 y + 1 = 0$ and $3 x - 5 y - 5 = 0$ and equally inclined to the axes.

Q. Find the equation of the line passing through the point of intersection of the lines 4 x + 7 y – 3 = 0 and 2 x – 3 y + 1 = 0 that has equal intercepts on the axes.

Join BYJU'S Learning Program

Find the equation of the lines which pass through the point of intersection of the line 4x−3y−1=0, 2x−5y+3=0 and are equally inclined to the axes

By 8(4)P.5, the slope of the line equally inclined to axes is tan(±45o)=±1. Hence by P+λQ=0,2λ+45λ+3=±1⇒λ=13,−1. Putting for λ, the two lines arex−y=0,x+y−2=0.

Find the equation of the lines which pass through the point of intersection of the line $4 x - 3 y - 1 = 0$ , $2 x - 5 y + 3 = 0$ and are equally inclined to the axes

By $8 (4) P .5$ , the slope of the line equally inclined to axes is $tan (\pm 45^{o}) = \pm 1$ . Hence by $P + λ Q = 0$ ,
$\frac{2 λ + 4}{5 λ + 3} = \pm 1$
$\Rightarrow λ = \frac{1}{3}, - 1$ . Putting for $λ$ , the two lines are
$x - y = 0, x + y - 2 = 0$ .