Question

Find the equations of the two lines drown through the point (-2,-1), which are inclined at 45° to the line y-2x=3 ?

Answer 1

y+1=x +2 and y+1= -x-2

Explanation:

Since both the lines are inclined at `45^0` to the given line, they would be perpendicular to each other. .

The slope of the given line is 2. Now, let slope of one of the required lines be 'm', then using the algebraic identity about the angle between two lines with slopes `m_1 and m_2`, it can be written as follows:

tan 45= `(m-2)/(1-2m)`

Hence m-2= 1-2m

Therefore m=1. The slope of one of the lines would be1 and slope of the other would be -1.

The equations, in the point slope form, would thus be y+1=1(x +2) and y+1= -1(x+2).