Question

Question 11 Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

Class X1 - Maths -Straight Lines Page 233

Answer 1

equation of line l₁ is
x - 2y = 3
so, slope of line l₁ is m₁ = 1/2

Let slope of line l₂ is m₂ = m

we know,
angle between two lines tanΘ = |m₂ - m₁|/|1+m₁.m₂|

Here , Θ = 45° , m₁ = 1/2 and m₂ = m
tan45°= | 1/2 - m |/|1 + m/2|
1 = |1 - 2m|/|m + 2 |
|m + 2| = | 1 - 2m |
(m + 2) = ± ( 1 - 2m)

taking negative sign,
(m + 2) = -(1 - 2m)
m + 2 = -1 + 2m
3 = m

taking positive sign,
( m + 2) = (1 - 2m)
m + 2 = 1 - 2m
3m = -1
m = -1/3

now, equation of line l₂ , passing through (3,2) and slope of it is 3 and -1/3
(y - 2) = 3(x - 3)
y - 2 = 3x - 9
y - 3x + 7 = 0

again,
( y - 2) = -1/3(x - 3)
3(y - 2) + (x - 3) = 0
3y - 6 + x - 3 = 0
x + 3y - 9 = 0