 # Can u give some shortcut formulas for straight lines???thnx....

9 years ago

There are not much so called "short cut " formulas! Use the various techniques which you have adopted in course of preperation at the exam hall to score well.

9 years ago

Analytical Geometry In A Nutshell
LINES - BASICS:

1. The equation of X axis: y =0
2. The equation of Y axis: x = 0
3. Equation of straight line parallel to X axis: y =a, where a is any constant
4. Equation of straight line parallel to Y axis: x =a, where a is any constant
5. Equation of a straight line through a given point (x1, y1) and having a given slope m: y -y1 = m (x - x1)
6. Equation of a straight line through a given point (0, 0) and having a given slope m: y = m x
7. Equation of a straight line with a slope m and y-intercept c is: y = mx + c
8. Equation of a straight line passing through two points (x1, y1) and (x2, y2) is:
(y -y1)/(y2 - y1) = (x -x1)/(x2 -x1)

9. Equation of a straight line whose x and y intercepts are a and b is:
x/a + y/b = 1

10. The length of the perpendicular drawn from origin (0,0) to the line Ax + By + C =0 is :
C/ sqrt(A^2 + B^2)

11. Length of the perpendicular from (x1, y1) to the line Ax + By + C =0 is:
Ax1 + By1 +C / sqrt(A^2 + B^2)
12. The point of intersection of two lines a1x + b1y +c1 = 0 and a2x + b2y +c2 = 0 is :
([b1*c2 - b2*c1]/[a1*b2 - a2*b1], [c1*a2 - c2*a1]/[a1*b2 - a2*b1])
13. The condition for concurrency of three lines a1x + b1y +c1 = 0, a2x + b2y +c2 = 0 and a3x + b3y +c3 = 0 is (in determinant form)
| a1 b1 c1 |
| a2 b2 c2 | = 0
| a3 b3 c3 |

14. The angle between two lines y = m1x + c1 and y = m2x + c2 is tan inverse of the modulus of :
[(m1 - m2)/(1 + m1*m2)]

15. Condition for parallelism of two lines with slopes m1 and m2 is m1 = m2
16. Condition for perpendicularity of two lines with slopes m1 and m2 is m1*m2 =-1