Question

If 4ab = 3h², then the ratio of slopes of the lines represented by the equation ax² +2hxy + by² = 0 will be ______

Options

• `sqrt2 : 1`

• `sqrt3 : 1`

• 2 : 1

• 1 : 3

Answer 1

If 4ab = 3h², then the ratio of slopes of the lines represented by the equation ax² +2hxy + by² = 0 will be 1 : 3.

Explanation:

Here, `m_1 + m_2 = (-2h)/b` ...................(i)

and m₁m₂ = `a/b`

∴ `(m_1 - m_2)^2 = (m_1 + m_2)^2 - 4m_1m_2`

= `(4h^2 - 4ab)/b^2`

= `(4h^2 - 3h^2)/b^2` ....................[∵ 4ab = 3h² (given)]

= `h^2/b^2`

∴ `m_1 - m_2 = h/b` ..................(ii)

On solving (i) and (ii), we get

`m_1 = (-h)/(2b) "and"  m_2 = (-3h)/(2b)`

∴ m₁ : m₂ = 1 : 3