Question

Family of curves which makes an angle $\frac{\pi }{4}$ whith the family of hyperbola xy = $C^2$ is

• A. x² – 4xy – y² = k
• B. x² + 2xy – y² = k
• C. x² – 2xy – y² = k
• D. x² + xy – y² = k

Answer 1

Answer: (B), (C)

The correct options are
B

x² + 2xy – y² = k

C

x² – 2xy – y² = k

$xy=c^2\Rightarrow \frac{dy}{dx}=m_1=\frac{-y}{x}{m}_2=\frac{dy}{dx}\Rightarrow \left|\frac{\frac{dy}{dx}+\frac{y}{x}}{1-\left(\frac{dy}{dx}\right)\left(\frac{y}{x}\right)}\right|=1\Rightarrow x^2+2xy-y^2=k\left(or\right)x^2-2xy-y^2=k$