Let C be the rose defined in polar coordinates as r = 2 cos(2), [0, 2]. (a) (6 Marks) Find all points (x(), y()) in C, for which the slope of the tangent line to C at (x(), y()) is equal to t (b) (4 Marks) Deduce from part (a) that there is no circle S with positive radius centered at the origin, for which C and S would intersect perpendicularly at some point. [Hint: For part (b), notice that if L is the straight line passing through the origin and a point (x(), y()) lying on a circle S centered at the origin, then L is perpendicular to S at (x(), y()), and it has the equation y = tan()x.]