Consider an astroid with parametric equations x=4cos3(t),y=4sin3(t)     (a) Find the slope of the tangent line to the astroid in terms of t. Slope =    (b) List all of the points (x,y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of xx, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y)= ( , ) Point 2: (x,y))= ( , ) Point 3: (x,y)= ( , )   (c) List all of the points (x,y) where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of xx. If two or more points share the same value of xx, list those points starting with the smallest value of yy. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y))= ( , ) Point 2: (x,y)= ( , ) Point 3: (x,y)= ( , )

Consider an astroid with parametric equations

(a) Find the slope of the tangent line to the astroid in terms of t.

Slope = 

(b) List all of the points (x,y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of xx, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them.

Point 1: (x,y)= ( , )

Point 2: (x,y))= ( , )

Point 3: (x,y)= ( , )

(c) List all of the points (x,y) where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of xx. If two or more points share the same value of xx, list those points starting with the smallest value of yy. If any blanks are unused, type an upper-case "N" in them.

Point 1: (x,y))= ( , )

Point 2: (x,y)= ( , )

Point 3: (x,y)= ( , )

(d) List all of the points (x,y)(x,y) where the slope of the tangent line is 1. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of xx, list those points starting with the smallest value of yy. If any blanks are unused, type an upper-case "N" in them.

Point 1: (x,y)= ( , )

Point 2: (x,y)= ( , )

Point 3: (x,y)= ( , )

(e) List all of the points (x,y) where the slope of the tangent line is -1. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of xx, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them.

Point 1: (x,y)= ( , )

Point 2: (x,y)= ( , )

Point 3: (x,y)= ( , )