Transcript Advanced Precalculus Notes 9.7 Plane Curves and Parametric
Advanced Precalculus Notes 9.7 Plane Curves and Parametric Equations
Plane curve: the collection of points (
x
,
y
) (
f
(
t
),
g
(
t
)) x = f(t) and y = g(t) over the same domain and where t is the parameter.
1 2
t
-2 -1 0
Discuss the curve defined by the parametric equations:
x
3
t
2
y
2
t
2
t
2
x y
Using the graphing calculator, graph the curve on your calculators.
Graphing Calculator: a) Press MODE and set the third line to Degree. You will work with angles in the second half of the chapter and those angles are measured in degrees. If you get a “funny” answer when using a trigonometric function, check to see that you are still in Degree mode.
b) Set the fourth line to Par. In this chapter your graph and use parametric equations. When you switch to Paramtetric mode, the Y = screen and the Window screen change.
c) Set the sixth line to Simul. In this chapter you graph more than one set of parametric equations. In Simultaneous mode, all equations graph at the same time, In Sequential mode, equations graph one after the other.
d) In Parametric mode the Window screen is different from the familiar Function mode Window screen. The Graph screen that you see is still set by the values of Xmin, Xmax, Xscl, Ymin, Ymax, Yscl. But in addition, you must set the starting and stopping values of t. The t-values you choose do not affect the dimensions of the Graph screen, but they do affect what will be drawn.
Find the corresponding rectangular equation by eliminating the parameter:
x
3
t
2
y
2
t
2
t
2
Find the rectangular equation of the curve whose parametric equations are:
x
a
cos
t y
a
sin
t a
0 0
t
2
Projectile motion:
x
(
v
0 cos )
t y
1 2
gt
2 (
v
0 sin )
t
h
Suppose that Jim hit a golf ball with an initial velocity of 150 feet per second at an angle of 30º to the horizontal.
a) Find parametric equations that describe the position of the ball as a function of time.
b) How long is the golf ball in the air?
c) When is the ball at its maximum height? Determine the maximum height of the ball.
d) Determine the horizontal distance that the ball traveled.
e) Graph using the calculator.
Kari runs an average velocity of 8 mph. Two hours after she leaves your house, you leave in your car and follow the same route. If your average velocity is 40 mph, how long will it be before you catch up to Kari?
Find parametric equations for the equation
y
x
2 4
Find parametric equations for the ellipse
x
2
y
2 9 1