Question

Find the orthogonal trajectories of the family of curves: 2 − 2 + 2 = 1, where is a parameter

Answer 1

Answer:

1. Let f(x,y,c)=0 be the equation of the given family of curves, where c is an arbitrary parameter.

2. Differentiate f=0; w.r.t. 'x' and eliminate c,ie, form a differential equation.

3. Substitute −

dy

dx

for

dx

dy

in the above differential equation. This will give the differential equation of the orthogonal trajectories.

4. By solving this differential equation, we get the required orthogonal trajectories.