Question

The transformed equation of x² + 6xy +8y² = 10, when the axes are rotated through an angle $\frac{\pi}{4}$ is

• A. 15x² – 14xy + 3y² = 20
• B. 15x² + 14xy – 3y² = 20
• C. 15x² + 14xy + 3y² = 20
• D. 15x² – 14xy – 3y² = 20

Answer 1

Answer: (C)

15x² + 14xy + 3y² = 20

Answer 2

x² + 6xy + 8y² = 10 .... (1)

Put $\begin{Bmatrix} x = x\cos\frac{\pi}{4} - y\sin\frac{\pi}{4} \\ y = x\sin\frac{\pi}{4} + y\cos\frac{\pi}{4} \end{Bmatrix}$ in equation (1)