Question

If x = X cosq – Ysinq, y = Xsinq + Ycosq& x² + 4xy + y²

= AX² + BY², 0 £ q £$\frac{\pi}{2}$ then

• A. A < B
• B. A = B
• C. | B | < | A |
• D. | A | < | B |

Answer 1

Answer: (C)

| B | < | A |

Answer 2

Putting values of x & y in given relation we get

(1 + 2sin2q)X² + 4cos2qXY + (1 – 2sin2q)Y²

= AX² + BY²

Comparing

cos2q = 0

Ž 2q = $\frac{\pi}{2}$

Ž q = $\frac{\pi}{4}$

Q 1 + 2sin2q = A

Ž A = 3

& B = – 1

\ | B | < | A |