JEE AdvancedHardQuestion 370009
Question
The orthogonal trajectories of the family of circles x² + y² = r² are:
- AStraight lines through the origin: y = kxCorrect
- BParabolas
- CEllipses
- DHyperbolas
Correct answer
Straight lines through the origin: y = kx
Explanation
Family of circles: x²+y²=r². DE: differentiate → 2x+2y(dy/dx)=0 → dy/dx=−x/y. For orthogonal trajectories, replace dy/dx with −y'/dx = −1/(−x/y) = y/x. New DE: dy/dx = y/x → ln y = ln x + C → y = kx (straight lines through origin).