Answer 1

Comparing the equation kx² + 4xy - y² = 0 with ax² + 2hxy - by² = 0, we get, a = k, 2h = 4, b = -1.

Let m₁ and m₂ be the slopes of the lines represented by kx² + 4xy - y² = 0 

∴ m₁ + m₂ = `(-2"h")/"b" = - 4/(-1) = 4`

and m₁m₂ = `"a"/"b" = "k"/(-1) = -"k"`

We are given that m₂ = m₁ + 8

∴ m₁ + m₁ + 8 = 4 

∴ 2m₁ = - 4    ∴ m₁ = - 2     ...(1)

Also, m₁(m₁ + 8) = - k

(-2)(- 2 + 8) = - k      ...[By (1)]

∴ (-2)(6) = - k

∴ - 12 = - k

∴ k = 12