Assignment:
Q(a) Find the orthogonal trajectories of the family of curves defined by
2cy + x2 = c2, c>0
State the differential equation of the orthogonal family, and show your steps in obtaining a solution.
Q(b) On the same set of "square" axes, plot at least five members of each of the given family and your family of orthogonal solutions.
Q(c) Identify one point of intersection, and approximate the coordinates of the point. Determine the slope of each curve at the point of intersection, and verify that the tangents are indeed perpendicular.
Provide complete and step by step solution for the question and show calculations and use formulas.