Question

Find k if,

the sum of the slopes of the lines represented by 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.

Now, m₁ + m₂ = 2(m₁m₂) ..(Given)