Orthogonal trajectory differential relation (At intersection, slopes multiply to -1. Replace dy/dx in the family's DE)

jee-mainjee-advanced

At intersection, slopes multiply to -1. Replace dy/dx in the family's DE by -1/(dy/dx) or swap to -dx/dy as convenient, then solve the new DE.

When to use this

Where slopes exist and are finite; handle horizontal/vertical tangents separately if needed.