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 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

[pdf-embedder url=”https://hemantmore.org/assets/2016/12/Pair-of-Straight-Lines-Unit-I-B.pdf” title=”Pair of Straight Lines Unit I B”]

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