,
Coordinate Geometry : parametric eqs.
 

[ introduction ][ example#1][ example#2 ][ example#3 ]

 

 

 

 

Introduction

There is another way of writing y as a function of x and that is to use two separate equations.

One equation has x as a function of t (or θ) eg x = 2t

and the other equation has y as function of t (or θ) eg y = t2

The variables t, θ are called parameters and the two equalities parametric equations.

Common questions on this topic are the plotting of parametric equations and their conversion to a single Cartesian equation.

Example #1

Plot the graph of the curve given parametrically by the equations:

x = 2cosθ         y = 2sinθ

θo

0

45

90

135

180

x = 2cosθ

2

1.414

0

-1.414

-2

y = 2sinθ

0

1.414

2

1.414

0

plotted circle

 

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Example #2

What is the Cartesian equation given parametrically by:

x = t2+3          y = t3 + 3t

 

parametric equation problem#1

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Example #3

What is the Cartesian equation given parametrically by:

x = 2sinθ          y = 2sin2θ

 

parameter problem#3

 

 

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