Question

If the angle between lines represented by ax² + 2hxy + by² = 0 is equal to the angle between lines represented by 2x² – 5xy + 3y² = 0 then show that 100(h² – ab) = (a + b)² .

Answer 1

The acute angle θ between the lines ax² + 2hxy + by² = 0 is given by

Comparing the equation 2x² – 5xy + 3y² = 0

with ax² + 2hxy + by² = 0, we get,

a = 2, 2h= -5, i.e. h = -5/2 and b = 3

Let ∝ be the acute angle between the lines

2x² – 5xy + 3y² = 0.

This is the required condition.