Pair of Straight Lines

Multiple choice questions collected from all Engineering Entrance Examinations (Click here)

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



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 .