Question

Find the separate equations of the lines represented by 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 m does not exist and and m₁ = \(\cfrac{3}{4}\).

Now, required lines are perpendicular to these lines.

Since these lines are passing through the origin, their separate equations are y = 0 and

∴ their combined equation is

y(4x + 3y) = 0 

∴ 4xy + 3y² = 0.