Question

If the sum of the slopes of the lines represented by x² + kxy + y² = 0 is four times their product, the value of k is ______.

Options

• – 8

• 8

• 4

• – 4

Answer 1

If the sum of the slopes of the lines represented by x² + kxy + y² = 0 is four times their product, the value of k is – 4.

Explanation:

Comparing x² + kxy + y² = 0 with

ax² + 2hxy + by² = 0, we get

a = 1, 2h = k, b = 1

∴ m₁ + m₂ = `(-2"h")/"b" = - "k"`

and m₁.m₂ = `"a"/"b"` = 1

According to the given condition,

m₁ + m₂ = 4m₁.m₂ 

⇒ – k = 4

⇒ k = – 4