4. Let C be the rose dened in polar coordinates as r = 2cos[26), 3 E [0, 2n]. (a) (6 Marks) Find all points (m(9),y(6)) in C, for which the slope of the tangent line to C at (53(6), y(t9)) is equal to tan(6). (b) (4 Marks) Deduce from part (a) that there is no circle S with positive radius centered at the origin, for which C and 5 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 (1:09), y()) lying on a circle S centered at the origin, then L is perpendicular to S at (1:09), y(6)), and it has the equation 3; = tan(9)-:r.]