Question

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

3x² − 4xy = 0 

Answer 1

Consider 3x² − 4xy = 0 

∴ x(3x − 4y) = 0

∴ separate equations of the lines are x = 0 and 3x − 4y = 0

Let m₁ and m₂ be the slopes of these lines.

Then m₁ does not exist and m₂ = `3/4`

Now, required lines are perpendicular to these lines.

∴ their slopes are `- 1/"m"_1` and `- 1/"m"_2`

Since m₁ does not exist, `- 1/"m"_1 = 0`

Also, m₂ = `3/4, - 1/"m"_2 = - 4/3`

Since these lines are passing through the origin, their

separate equations are y = 0 and y = `- 4/3`x, i.e. 4x + 3y = 0

∴ their combined equation is

y(4x + 3y) = 0

∴ 4xy + 3y² = 0