Question

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then ______ 

Options

• 8h² = 9ab

• 8h² = 9ab²

• 8h = 9ab

• 8h = 9ab²

Answer 1

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then 8h² = 9ab.

Explanation:

Given equation of pair of lines is

ax² + 2hxy + by² = 0

∴ m₁ + m₂ = `(-2h)/b` and m₁m₂ = `a/b`

According to the given condition,

m₁ = 2m₂

∴ 2m₂ + m₂ = `(-2h)/b` and 2m₁m₂ = `a/b`

∴ m₂ = `(-2h)/(3b)` and `m_2^2 = a/(2b)`

∴ `((-2h)/(3b))^2 = a/(2b)`

∴ `(4h^2)/(9b^2) = a/(2b)`

∴ 8h² = 9ab