Answer
See below.
Work Step by Step
a) The orthogonal trajectory of a family of curves is defined as a set of curves that intersects each curve of the family orthogonally or at right angles.
b) The steps to describe the orthogonal trajectory of a family of curves are discussed below:
i) Firstly, we will construct a differential equation $F(x,y)=0$ for the given family of curves.
ii) Then, we take the negative reciprocal of the differential equation $f(x,y)=\dfrac{dy}{dx}$.
iii) We simplify the new differential equation to compute the algebraic equation of the family of orthogonal trajectories $F(x,y)=C$.
