Question

Find k, if the slope of one of the lines given by 3x² + 4xy + ky² = 0 is three times the other.

Answer 1

Comparing the equation 3x² + 4xy + ky² = 0 with ax² + 2hxy + by² = 0, we get, 

Let slopes of the lines represented by 3x² + 4xy + ky² = 0 be m and 3m.

a = 3, 2h = 4, b = k

Let m₁ and m₂ be the slopes of the lines represented by 3x² + 4xy + ky² = 0

∴ m₁ + m₂ = `(-2"h")/"b" = -4/"k"`

and m₁m₂ = `"a"/"b" = 3/"k"`

Now, m₁ + m₂ = 3(m₁m₂)     ......(Given)

∴ `(-4/"k") = 3(3/"k")`