Contour Plot

Creating a contour plot

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl', 'PGML.pl', 'parserPopUp.pl', 'PGtikz.pl',
    'PGcourse.pl'
);

$showPartialCorrectAnswers = 0;

Preamble

We will use PGtikz.pl for constructing the graph. The macro parserPopUp.pl is used to include the popup.

$graph = createTikZImage();
$graph->tikzLibraries('arrows.meta');
$graph->BEGIN_TIKZ
\tikzset{>={Stealth[scale=2]}}
\Large % Make the fonts a little bigger.
\filldraw[
    draw=LightBlue,
    fill=white,
    rounded corners=10pt,
    thick,use as bounding box
] (-7,-7) rectangle (7,7);
\foreach \n in {0,...,7} {
    \pgfmathsetmacro\k{100-\n*10}
    \filldraw[fill=blue!\k!white,fill opacity=0.5]
        (0,0) circle [radius={sqrt(64-8*\n)}];
}
\draw[->] (-7,0) -- (7,0) node[above left,outer sep=3pt] {\(x\)};
\foreach \x in {-6,...,-1,1,2,...,6}
    \draw(\x,5pt) -- (\x,-5pt) node [below] {\(\x\)};
\draw[->] (0,-7) -- (0,7) node[below right,outer sep=3pt] {\(y\)};
\foreach \y in {-6,...,-1,1,2,...,6}
    \draw (5pt,\y) -- (-5pt,\y) node[left] {\(\y\)};
END_TIKZ

$popup = DropDownTF('false', placeholder => 'Select One');

Setup

The contour plot is created with TikZ by overlaying circles with differing shades of blue. See the POD and the TikZ manual for more information.

If the colored contour plot is not desired, replace the \filldraw line with the following:

 \draw (0,0) circle [radius={sqrt(64-8*\n)}];

BEGIN_PGML
Determine if the following statement is true or false.

[_]{$popup} This could be a contour plot for [`f(x,y) = x^2 - y^2`].

>> [@ image($graph, width => 300, height => 300, tex_size => 450) @]* <<
END_PGML

Statement

This is the problem statement in PGML.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.