Pair of Straight Lines

Important Formulas :

1. General equation of a pair of straight lines is 

2. If   be an equation of pair of straight lines. Slope of first line 

And slope of the second line 

3. 

And 

4.  and  are  real and distinct , if  

5.  and  are coincident,  if  

6.  and  are imaginary, if  

7. Angle between the pair of lines is given  by 

8. If lines are coincident, then .

9. If lines are perpendicular, then .

10. The joint equation of bisector of the angles between the lines represented  by the equation  is  

11. The necessary and sufficient condition  to represent a pair of straight lines, if    or 

12. The equation of the bisectors of the angles between the lines represented by   are given by 

13. where   is the point of intersection of the lines represented by given equation.

14. The general equation   will represent two parallel lines, if  and  and the distance between  them  is 

15. If the equation of a pair of straight lines is  , then the point of intersection is given by 

16. The equation of the pair of lines through the origin and perpendicular to the pair of the lines given by   is 

17. Equation of the straight lines having the origin to the points of intersection of a second degree curve   and a straight line  is    

18. If  and  are the mid -point  of the sides  and  of  , then the centroid of centroid of .

19. Orthocentre of the right angled , right angled at  is .

20. The distance of a point  from the  is 

21. Distance between two parallel lines  and  is given by 

22. The area of triangle formed by the lines  and  is 

23. The length of perpendicular from a point  to the line  is 

24. Three given points  are collinear i.e. lie on the same straight line, if any of yhr three points (say B) lie on the straight line joining the other two points. 

25. Area of the triangle formed by the line  with the coordinate axes is 

26. The foot of the perpendicular  from  to the line  is given by 

27. Area of rhombus formed by .

28. Area of the parallelogram formed by the lines  and  is 

29. Foot of perpendicular form  on  is 

30. Foot of perpendicular form  on  is 

31. The image of the line  about the line  is 

32. Given two vertices   and  of an equilateral , then its third vertex is given by 

33. The equation of the straight line which passes through a given point  and makes an angle  with the given straight line  are  

34. The equation of the family  of lines passing through the intersection of the lines  and  is 

Where  is any real number :

35. Line  divides the line joining the points   and  in the ratio  then 

36. If   is positive it divides internally and if  is negative, then it divides externally.

37. Area of a polygon n-sides with vertices 

38. Equation of the pair of lines through  and perpendicular to the pair  of lines  is .

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