Question

Show that the slopes of the lines represented by 3x² – 4xy + y² = 0 differ by 2.

Answer 1

3x² – 4xy + y² = 0

Here, a = 3,

b = 1,

h = – 2

Let m₁ and m₂ be the slopes of given lines.

∴ m₁ + m₂ = `-(2h)/b` = 4   .....(1)

and m₁m₂ = `a/b` = 3   ......(2)

Now (m₁ – m₂)² = (m₁ + m₂)² – 4m₁m₂

= (4)² – 4(3)   ...[From (1) and (2)]

= 16 – 12

= 4

∴ m₁ – m₂ = ± 2

∴ |m₁ – m₂| = 2