a. Plot the two families of curves on the same set of axes, family1 = x^2+y^2=a*x (use several values of a between -4 and 4) and family2 = x^2+y^2=b*y (use several values of b between -4 and 4). Use a viewing window of x=-5..5,and y=-5..5.
b. Find (in terms of a and b) the point(s) of intersection between any curve in family1 and any curve in family2.
c. Use implict differentiation on Maple to prove that these two families are orthogonal trajectories of each other (see section 3.6), ie that the tangent lines at any point of interesection are perpendicular.
d. Plot the curves when a = 2 and b =3, together with their tangent lines at the point in the 1st quadrant where they intersect. Use the plot option scaling=constrained so you can see that the tangent lines are indeed perpendicular.