Question

The sum of the slopes of the lines given by x² – 2λxy – 7y² = 0 is 4 times their product, then the value of λ is ______.

Options

• 2

• – 1

• 1

• – 2

Answer 1

The sum of the slopes of the lines given by x² – 2λxy – 7y² = 0 is 4 times their product, then the value of λ is 2.

Explanation:

x² – 2λxy – 7y² = 0

Here a = 1, 

h = –λ,

b = –7

Given: m₁ + m₂ = 4m₁m₂

i.e. `(-2h)/b = (4a)/b`,

i.e. –2h = 4a

∴ –2(–λ) = 4(1)

i.e. 2λ = 4,

∴ λ = 2