Question

Find 'k' if the sum of slopes of lines represented by equation x² + kxy − 3y² = 0 is twice 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 = `(-2h)/b = -k/((-3)) = k/3`

and m₁m₂ = `a/b = 1/((-3)) = -1/3`

Now, m₁ + m₂ = 2(m₁m₂) ..(Given)

∴ `k/3 = 2(-1/3)`

∴ k = −2