Question

Find k, if the sum of the slopes of the lines given by x² + kxy − 3y² = 0 is equal to their product.

Answer 1

Comparing the equation x² + kxy − 3y² = 0 with ax² + 2hxy + by² = 0, we get,

a = 1, 2h = k, b = −3

Let m₁ and m₂ be the slopes of the lines represented by x² + kxy − 3y² = 0.

∴ m₁ + m₂ = `(− 2"h")/"b" = (−"k")/(−3) = "k"/3`

m₁m₂ = `"a"/"b" = 1/(−3) = (−1)/3`

Now, m₁ + m₂ = m₁m₂     ...(Given)

∴ `"k"/3 = (−1)/3`

∴ k = −1.