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 .