Find the condition that the diagonals of the parallelogram formed by the lines 
a x + b y + c = 0 ;   a x + b y + c ' = 0 ;   a ' x + b ' y + c = 0   &   a ' x + b ' y + c ' = 0  are at right angles. Also find the equation to the diagonals of the parallelogram.

dear student

if diagonals of parallelogram are at right angles, then it is rhombus
distance between ax+by+c=0 and ax+by+c'=0=distance between a'x+b'y+c=0 and a'x+b'y+c'=0c-c'a2+b2=c-c'a'2+b'2soa2+b2=a'2+b'2
then in this case, the distance between the parallel lines must be the same.



regards
 

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