Question

Find the relation between a
lation between a, b, a' and b' such that the two lines ax + by= c and a'x + b'y = c' are perpendicular
​

Answer 1

Answer:

a a' + b b' = 0

Step-by-step explanation:

Given :

Equation of first line :

a x + b y = c

= > a x + b y - c = 0

Slope of line = - A / B

= > m₁ = - a / b

Equation of second line :

a'x + b'y = c'

= >  a'x + b'y - c' = 0

Slope of line = - A / B

= > m₂ = - a' / b'

We know if two line are perpendicular then their slope product is - 1 .

i.e. m₁ m₂ = - 1

Putting values of m₁ and m₂ here :

= > ( - a / b ) ( - a' / b' ) = - 1

= > a a' = - b b'

= > a a' + b b' = 0

Therefore we get required relation.