Question

If the axes are rotated through an angle of 45⁰ in the anti clockwise direction then the equation of rectangular hyperbola x² – y² = a² changes to

• A. xy = a²
• B. xy = 2a²
• C. 2xy = a²
• D. 2xy + a² = 0

Answer 1

Answer: (D)

2xy + a² = 0

Answer 2

x = Xcos45⁰ – Ysin45⁰ = $\frac{X - Y}{\sqrt{2}}$

y = Xsin45⁰ + Ycos45⁰ = $\frac{X + Y}{\sqrt{2}}$

∴ The transformed equation of x² – y² = a² is

$\left( \frac{X - Y}{\sqrt{2}} \right)^{2} - \left( \frac{X + Y}{\sqrt{2}} \right)^{2} = a^{2}$

⇒ 2xy + a² = 0