IIT JEE , AIEEE Forum - Articles Category , Community shelf - Analytical geometry made easy!!!!!!!!!!!!!

KAB

Here are some shortcuts which you should never ever forget!

1)Area of the triangle made by the line ax+by+c=0 and the co ordinate axes is c²/(2ab)

2)Area of the rhombus formed by ax(+or-)by(+or-)c=0 is 2c²/ab

3)If ABCD is parallelogram

then D=A-B+C

Eg:If (1,6),(2,5),(5,1) are three vertices of a parallelogram

then fourth vertex is (1-2+5,6-5+1) ie(4,2)

4)The foot of the perpendicular (h,k) from (x₁,y₁) to the line ax+by+c=0 is given by

(h-x₁)/a=(k-y₁)/b= -(ax₁+by₁+c)/(a²+b²)

5)The image or reflection of the point (x₁,y₁) in the line ax+by+c=0 is (h,k) where

(h-x₁)/a=(k-y₁)/b= -2(ax₁+by₁+c)/(a²+b²)

(4) and 5) can be applied to 3-D geometry too!)

6)The area bounded by y²=4ax andx²=4by is given by (4a)(4b)/3

7)The area bounded by y²=4ax and the line y=mx is 8a²/(3m³)

8)The area bounded by y²=4ax and its latus rectum x=a is 8a²/3

I hope this is helpful!