consider the graph of the curve with parametric equations x(t)=-3 sin(2t), y(t)=4 cos(2t) for t or equal to 0. sketch graph of curve indicate the...

consider the graph of the curve with parametric equations x(t)=-3 sin(2t), y(t)=4 cos(2t) for t > or equal to 0.

a. sketch graph of curve indicate the direction of increasing t.

b. Find slope of line tangent to the graph of this curve when t = pi/6.  (use dy/dx =(dy/dt)/(dx/dt) )

c. show that (x^2/9)+ (y^2/16) =1. A Curve with this equation is called an _______

d. By using implicit differentiation on the equation in c, find dy/dx in terms of x and y. Calculate x(pi/6) and y(pi/6), and reconcile your answer to part b