What is a Parameter?
What is the purpose of the parameter ttt in a parametric equation?
To define both x and y
What point is generated by x = t + 1, y = 2t − 3 when t = 2?
(3, 1)
What rectangular equation results from x = t + 2 and y = 3t − 1?
y = 3x − 7
For x = t, y = t², in what horizontal direction does the particle move as t increases?
Left to right
What curve is represented by x = t, y = 2t + 1?
Line
What information does a parametric equation provide that a rectangular equation does not?
Direction of motion
What point is generated by x = t², y = t³ when t = −2?
(4, −8)
What rectangular equation results from x = t² and y = t?
x = y²
For x = cos t, y = sin t, what direction is the unit circle traced?
Counterclockwise
What curve is represented by x = t, y = t²?
Parabola
Why can different parametric equations represent the same curve?
Due to equations that produce the same graph but trace it in a different way, direction, or speed = Different parametrizations
What values of t produce the point (4, 2) for x = t², y = t?
2
What rectangular equation results from x = cos t and y = sin t?
x² + y² = 1
For x = cos t, y = −sin t, what direction is the unit circle traced?
Clockwise
What curve is represented by x = cos t, y = sin t?
Circle
What happens to the graph if the interval of t is restricted?
Only part of the curve is traced
What point is generated by x = cos(π), y = sin(π)?
(−1, 0)
What rectangular equation results from x = 2t − 1 and y = t²?
y=(x+1 / 2)2
What tool is commonly used to determine direction of motion on a parametric graph?
A table of t-values
What curve is represented by x = t², y = t² + 3?
Line
What characteristic of a particle's motion can change while the curve remains unchanged?
Direction or speed
What point is generated by x = t² + 1, y = t² − 3 when t = −2?
(5, 1)
What rectangular equation results from x = t² + 1 and y = t² − 3?
y = x − 4
Why can't a rectangular equation alone determine direction of motion?
It contains no parameter
What curve is represented by x = 3cos(t), y = 2sin(t)?
Ellipse