IAS Civil Exam, UPPSC Entrance Preparation, Civil Services Tests Online,Disscussion Forum

CyBorG

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!