Parametric Equations

Question 1

How do you eliminate the Parameters in: x = f(t) ; y = g(t) ??

Answer 1

Substitute ‘t’ into y for x and form the Cartesian equation.

Question 2

Example 1: Describe the curve defined by the parametric equations: x(t) = t - 3 ; y(t) = 5 - 2t

Answer 2

y = -2x - 1

Question 3

Example 2: The positions of a particle is given by: x = cos2A ; y = sin2A a)Graph the curve and indicate orientaion b)Mark on your Graph the particles positon when A = pi/6 and A = pi/3 c)Determine the Cartesian equation

Answer 3

a & b make graph c) x^2 + y^2 = 1

Question 4

dy/dx of a parametric equations of x(t) and y(t) = ???

Answer 4

dy/dx = (dy/dt) / (dx/dt)

Question 5

d^2y/dx^2 = ????

Answer 5

d/dx(dy/dx) / dx/dt

Question 6

Example 3: a) Eliminate t in the following equations to determine the type of curve represented: x = cos(t) ; y = 1 - cos2(t)

Answer 6

y = 2(1 - x^2)

Question 7

The parametric equations of a cycloid are: x = 2(A - sinA) ; y = 2(1 - cosA) Determine 2 points where the tangent to this cycloid is vertical.

Answer 7

A = 0, 2π