Planar curves are given in one of the three forms - explicitly as
in 
(a parabola), implicitly as in 
(a circle), or
in parametric form as in 
, 
(a cycloid). Curves may also be given in polar form as in the three
leaved rose 
.
To draw two explicitly given curves 
and y=1-2x over
the interval [0,1], use
plot( {x-x^2, 1-2*x}, x=0..1 );
To determine the point of intersection of the two curves in
0<x<1, left click the point of intersection to obtain
its approximate location as 
. To kill the graph
type q in the graph window.
To draw curves given in parametric form one still uses the plot command.
e.g. to plot the cycloid 
, and the
circle with center origin and radius 2 given in parametric form by
use
plot( {[t+sin(t), 1-cos(t), t=-6..6], [2*cos(t), 2*sin(t), t=0..7]} );
The circle does not really look circular.
In the graph window, from Projection choose Constrained to get
the true shapes of the graphs.
The ranges 
and 
were chosen somewhat
arbitrarily. What is the effect of decreasing or increasing these ranges?
Try it - and observe what is happening and why.
To draw curves given implicitly ( i.e. they are not given in the form
, but in the form 
) use the implicitplot command.
However,
this command is in the plots package. So to draw the ellipses
and 
use
with(plots); Load the plots package - only once in a Maple session
implicitplot( {x^2 + y^2 = 1, 4*x^2 + y^2 = 2}, x=-1..1, y=-2..2 );
Again the approximate locations of the points of intersection may be read
of with the help of the pointer. Some remarks are in order here.
bullistitem The plot command needs only the x range, which is determined
by the region of interest.
However, the implicitplot command needs the x and the y ranges.
Only that part of the graph will be drawn which fits inside the rectangle
determined by the range. One may choose the correct range by experimentation.
Curves which can be plotted using plot may also be plotted
using implicitplot but not vice versa. Wherever possible use
plot instead of implicitplot because plot is faster
and one does not need the y range for it (which may be hard to determine).
Notice the use of the curly brackets {} when plotting two or
more curves - all the equations/functions being plotted must be enclosed
in these curly brackets. These curly brackets are not necessary
(but may be used) when plotting a single curve.
To plot curves given in polar coordinates use the command polarplot
in the plots package.
To draw the circle 
(with 
) and the cardiod 
(with 
) in the same picture, use
with(plots);
polarplot( { [cos(t), t, t=0..Pi], [1+cos(t), t, t=0..2*Pi] } );
Here we have used the symbol t instead of 
.
In the plot window choose Constrained from Projection.
To superimpose two plots (obtained from different commands) use the
display command in the
plots package. e.g. to display the graphs of 
and the
cardiod 
in the same picture. Use
with(plots):
pic1 := plot( x/2, x=-1..4, color=red ): Note the : sign
pic2 := polarplot( [1+2*cos(t), t, t=0..2*Pi], color=green ):
display( {pic1,pic2} );
The second and third lines define two pictures pic1 and
pic2 - note the : used in the two lines.
We don't display their results because pic1 and pic2 are
stored algebraically (instead of pictorially) and are quite a mess
(change : to ; and see what happens - then scroll back and fix it).
The last line displays the two pictures - superimposed.
