collections from previous goiit articles :
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