Part 2/6:
An orthogonal trajectory involves two families of curves that intersect at right angles at every point. To illustrate this, consider a family of curves represented as equations, where one example is the quadratic family defined as ( y = k \cdot x^2 ). Here, 'k' is a constant that changes, allowing for a variety of curves that share a common structure.
Example: Circles and Lines
To visualize orthogonal trajectories, let’s consider the family of curves represented by the equation of circles ( x^2 + y^2 = R^2 ), where ( R ) denotes the radius of the circle. As you change the value of ( R ), you obtain different circles centered at the origin.