Find the joint equation of lines:Passing through the origin and perpen

1.	Find the joint equation of lines:Passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18.
Answer» Let L₁ and L₂ be the lines passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18 respectively. Slopes of the lines x + 2y = 19 and 3x + y = 18 are -1/2 and -3/1 = -3 respectively. Since the lines L₁ and L₂ pass through the origin, their equations are y = 2x and y = 1/3 x i.e. 2x – y = 0 and x – 3y = 0 ∴ their combined equation is (2x – y)(x – 3y) = 0 ∴ 2x² – 6xy – xy + 3y² = 0 ∴ 2x² – 7xy + 3y² = 0.

Find the joint equation of lines:Passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18.

Answer»

Let L₁ and L₂ be the lines passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18 respectively.

Slopes of the lines x + 2y = 19 and 3x + y = 18 are -1/2 and -3/1 = -3 respectively.

Since the lines L₁ and L₂ pass through the origin, their equations are

y = 2x and y = 1/3 x

i.e. 2x – y = 0 and x – 3y = 0

∴ their combined equation is

(2x – y)(x – 3y) = 0

∴ 2x² – 6xy – xy + 3y² = 0

∴ 2x² – 7xy + 3y² = 0.