Question

The difference between the slopes of lines represented by 6x² – 5.xy + y² = 0 is ______.

Options

• 1

• 2

• 3

• 4

Answer 1

The difference between the slopes of lines represented by 6x² – 5.xy + y² = 0 is 1.

Explanation:

Given equation of lines is

6x² – 5.xy + y² = 0

∴ a = 6, b = 1, 2h = – 5

∴ m₁ + m₂ = `(-2"h")/"b"` = 5

m₁m₂ = `"a"/"b"` = 6

Now, (m₁ – m₂)² = (m₁ + m₂)² – 4m₁m₂

⇒ (m₁ + m₂)² = 5² – 4(6)

⇒ (m₁ + m₂)² = 1

⇒ m₁ – m₂ = 1