Question

Prove that the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by ax² + 2hxy + by² = 0 is bx² – 2hxy + ay² = 0

Answer 1

Let m₁ and m₂ be the slopes of the lines represented by ax² + 2hxy + by² = 0.

Now, required lines are perpendicular to these lines.

∴ their slopes are -1/m₁ and -1/m₂

Since these lines are passing through the origin, their separate equations are