**Type – I B **

## 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 m_{1} and m_{2} 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

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