Provide an appropriate response.(a) Graph the curves r = and r = .(b) Find polar coordinates of the points of intersection of the curves in part (a).(c) Show that at the points of intersection the tangent lines to the curves are perpendicular to each other.

Question

What will be an ideal response?

Answer 1

(a)

(b) The curves intersect in two points. In polar coordinates, these points may be represented by  and .
(c) For r = ,  = -cot . For r = ,  = tan . Thus the slopes of the tangent lines to the curves at both of the points of intersection are negative reciprocals of each other so the tangent lines are perpendicular.