Straight Lines

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