Question

If one of the lines given by ax² + 2hxy + by² = 0 is perpendicular to px + qy = 0 then show that ap² + 2hpq + bq² = 0.

Answer 1

To prove ap² + 2hpq + bq² = 0.

Let the slope of the pair of straight lines ax² + 2hxy + by² = 0 be m₁ and m₂

Then, m₁ + m₂ = \(\cfrac{-2h}{b}\) and m₁m₂ = \(\cfrac{a}{b}\)

Slope of the line px + qy = 0 is \(\cfrac{-p}{q}\)

But one of the lines of ax² + 2hxy + by² = 0 is perpendicular to px + qy = 0