Question

If pair of straight lines ax² + 2hxy + by² = 0 is rotated by an angle of 90° about origin then their equation in new position are given by –

• A. ax² + 2hxy + ay² = 0
• B. ax² –2hxy – by² = 0
• C. bx² + 2hxy + ay² = 0
• D. bx² –2hxy + ay² = 0

Answer 1

Answer: (D)

bx² –2hxy + ay² = 0

Answer 2

Let (ax² + 2hxy + by²) = (y – m₁x) (y – m₂x)

\ m₁+ m₂ =, m₁m₂ = a/b

New lines will be

(x + m₁y) (x + m₂y) = 0

x² + (m₁ + m₂)xy + m₁m₂y² = 0

Put values of m₁ + m₂ and m₁m₂