Find the condition that the diagonals of the parallelogram formed by the lines ax+by+c=0; ax+by+c'=0; a'x+b'y+c=0 a'x+b'y+c'=0 - Maths - Straight Lines

Question

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

Rahul Raj · Accepted Answer

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

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.

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.