The orthogonal trajectory of the family of straight lines y = mx is given by:

The orthogonal trajectory of the family of straight lines y = mx is given by:

• A. x² + y² = c²
• B. xy = c
• C. x² − y² = c²
• D. y² = cx

Answer: A) x² + y² = c²

Explanation: Differentiate y = mx to get DE: dy/dx = y/x. For orthogonal trajectories, replace dy/dx with −dx/dy. So, −dx/dy = y/x → x dx + y dy = 0. Integrating gives x²/2 + y²/2 = k → x² + y² = c², representing circles.