Question

Find the joint equation of pair of lines passing through the origin and perpendicular to the lines represented by ax²+ 2hxy + by²= 0

Answer 1

Given equation is ax² + 2hxy + by² = 0,
Let m₁ and m₂ be the slopes of the given lines

`∴ m_1+m_2=(-2h)/b and m_1m_2=a/b`

Since, the required lines are perpendicular to these lines

∴ slopes of the required lines are `-1/m_1 and -1/m_2`

Required lines also pass through the origin, therefore their equations are

`y=-1/m_1x and y=-1/m_2x`

∴ the joint equation of the lines is `(x+m_1y)(x+m_2y)=0`

`∴ x^2+(m_1+m_2)xy+m_1m_2y^2=0`

`∴ x^2+((-2h)/b)xy+(a/b)y^2=0`

`∴ bx^2-2hxy+ay^2=0`