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

#### Important Formulas:

SLOPE OF LINE:

1. Let and be any two points.

2. The slope of the line joining and is defined as

3. where is the angle which the line makes with the positive direction of the x-axis, except at

4. Which is possible only if and the line is parallel to the y-axis.

STANDARD FORMS OF THE EQUATION OF A LINE:

5. An equation of a line parallel to the x-axis is and that of the x-axis itself is

6. An equation of a line parallel to the x-axis is and that of the x-axis itself is

7. An equation of a line passing through the origin and making an angle with the positive direction of the x-axis is

8. An equation of a line passing through the origin having a slope is

9. An equation of a line passing through the origin Passing through the point is

10. Slope-Intercept form: An equation of a line with slope and making an intercept on the y-axis is

11. Point-Slope form An equation of a line with slope and passing through is .

12. Two - Point form: An equation of a line passing through the points and

13. Intercept form: an equation of a line making intercepts and on the x-axis and y-axis respectively, is

14. Parametric corm: An equation of a line passing through a fixed point and making an angle with the positive direction of the x-axis is

15. where is the distance of an arbitrary point on the line from the point . Note that and

16. Normal form: An equation of a line such that the length of the perpendicular from the origin on it is and the angle

17. which this perpendicular makes with the positive direction of the x-axis is is

18. General form : In general , an equation of a straight line is of the form , where and are real numbers, and both cannot be zero simultaneously.

19. The slope is

20. The intercept on the x-axis is and the intercept on the y-axis is

21. and , the positive sign being taken if is negative and vice versa.

22. If denotes the length of the perpendicular from on this line, then

23. The points and lie on the same side of the line if the expressions have the same sign, and on the opposite side if they have the opposite signs.

TWO OR MORE LINES:

24. Two lines given by the equations and are parallel (i.e., the slopes are equal), if

25. Two lines given by the equations and are perpendicular(i.e., the product of their slopes is -1), if

26. Two lines given by the equations and are identical if

27. Two lines given by the equations and are not parallel, then angle between them at their point of intersection is given by being the slopes of the two lines.

28. Two lines given by the equations and are not parallel, then the coordinates of their point of intersection are

29. Two lines given by the equations and are not parallel, then an equation of any line through their point of intersection is where is a non zero finite real number.

30. An equation of a line parallel to the line is and the distance between these lines is

31. Three lines and are (intersect at a point) if and only if

32. Equations of the bisectors of the angles between two intersecting lines and are

33. Equations of the lines through and making an angle with the line are where and where

for_StraightLines