Q. 114.2( 41 Votes )
Find the equation of the lines through the point (3, 2) which make an angle of 45o with the line x – 2y = 3.
Let the slope of the required line be m1.
The given line can be written as , which is of the from y = mx + c
Thus, Slope of the given line = m2 =
It is given that the angle between the required line and line x – 2y = 3 is 45o.
We know that if Ɵ is the acute angle between lines l1 and l2 with slopes m1 and m2 respectively, then
⇒ 2 + m1 = 1- 2m1 or 2 + m1 = -1 + 2m1
⇒ m1 = or m1 = 3
Now, when m1 = 3, then,
The equation of the line passing through (3,2) and having a slope of 3 is:
y – 2 = 3(x – 3)
⇒ y -2 = 3x – 9
⇒ 3x – y = 7
And, when m1 =
The equation of the line passing through (3,2) and having a slope of is:
3y – 6 = -x + 3
x + 3y = 9
Therefore, the equations of the lines are 3x – y = 7 and x + 3y = 9.
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