Let C be the rose defined in polar coordinates as r= 2 cos(20), 8 [0, 2]....

 

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Let C be the rose defined in polar coordinates as r= 2 cos(20), 8 [0, 2π]. (a) (6 Marks) Find all points (r(0), y(0)) in C, for which the slope of the tangent line to Cat (r(0), y(0)) is equal to tan(0). (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(0), y(0)) lying on a circle S centered at the origin, then L is perpendicular to S at (x(0), y(0)), and it has the equation y = tan(0)-2.] Let C be the rose defined in polar coordinates as r= 2 cos(20), 8 [0, 2π]. (a) (6 Marks) Find all points (r(0), y(0)) in C, for which the slope of the tangent line to Cat (r(0), y(0)) is equal to tan(0). (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(0), y(0)) lying on a circle S centered at the origin, then L is perpendicular to S at (x(0), y(0)), and it has the equation y = tan(0)-2.]