Question

1) A particle is moving on a curve that has the parametric equations x=-4cost, y=5sint, 0≤?≤2?.

a) Find dy/dx when t= pi/4.

b) Eliminate the parameter t to find a cartesian (x, y) equation of the curve and recognize it.

c) Graph the Cartesian equation and indicate the direction of the motion.

Answer 1

we are given

parametric equation as

x=-4cost, y=5sint

(a)

we can find derivative

now, we can find dy/dx

now, we can plug it

now, we can plug t=pi/4

............Answer

(b)

x=-4cost, y=5sint

now, we can use trigonometric identity

Hence,

this is equation of ellipse

(c)

Graph: