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

The PGtikz.pl macro is used for constructing the graph. The parserPopUp.pl macro is used for a drop down menu answer.

$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 PGtikz.pl and the TikZ manual for more information.

If a filled and colored contour plot is not desired, replace the \filldraw line in the \foreach loop with

\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.