## When Angles Made by the Lines with X/Y axis are Given

Problems shown in RED color are for Last Minute Revision (LMR)

ALGORITHM:
1. If θ is the inclination of a line, then its slope is given by m = tan θ.
2. Find slopes m1 and m2 of the two lines.  maths, mathematics, co-ordinate geometry
3. Use y = mx form to find equations of the two lines.
4. Write equations of lines in the form u = 0 and v = 0.
5. Find u.v = 0.
6. Simplify the L.H.S. of joint equation.

### Examples for Practice

1. Find the combined equation of the lines passing through the origin and making an angle of 30o with positive direction of x – axis
2. Find the combined equation of the lines passing through the origin and making an angle of 45o  with positive direction of x – axis
3. Find the combined equation of the lines passing through the origin and making an angle of 60o with positive direction of x – axis
4. Find the combined equation of the lines passing through the origin and making an angle of 60o with y – axis
5. Find the joint equation of a pair of lines through the origin having  inclinations 30and 150o.
6. Find the joint equation of a pair of lines through the origin having inclinations 60and 120o. (MSB Text)
7. Find the joint equation of a pair of lines through the origin having and having inclination Π/3 and 5Π/3.

## Solution

Pair of Straight Lines Unit I B