3.7 Plotting Implicitly Defined Functions

An implicitly defined function is given as an equation relating two variables, such as x ² + y ² = 1 (which describes a circle of radius one). Here the y variable is not given explicitly as a function of the x variable, but rather the x and y terms are wrapped up in an equation; hence the term implicitly defined function. In order to plot an implicitly defined function, use the ContourPlot command. Use the implicit equation for the first argument (with a double equal sign == either typed from the keyboard or inserted via the BasicMathInput palette), and include two iterators: one for x, a second for y.

  In[1]:= <b class="bold">ContourPlot[x</b><sup<b class="bold">2</b></sup> <b class="bold">+</b> <b class="bold">y</b><sup<b class="bold">2</b></sup> <b class="bold">==</b> <b class="bold">1, {x, <span class="unicode">?</span>1, 1}, {y, <span class="unicode">?</span>1, 1}]</b><span class="inlinemediaobject"><a NAME="IMG_182"> href="portalcontent.asp?bkid=31099&image_src=https://images.books24x7.com/bookimages/id_31099/fig110%5F01%5F0%2Ejpg&image_id=182&previd=IMG_182"> target="_parent"><img alt="Image from book"> border="0"> height="227"> id="IMG_182"> src="https://images.books24x7.com/bookimages/id_31099/fig110_01.jpg"> title="Click To expand"> width="290"></a></span>

By default, a ContourPlot will display with a frame and no coordinate axes, but it is a simple matter to change this behavior.

  In[2]:= <b class="bold">ContourPlot[x</b><sup<b class="bold">2</b></sup> <b class="bold">+</b> <b class="bold">y</b><sup<b class="bold">2</b></sup> <b class="bold">==</b> <b class="bold">1, {x, <span class="unicode">?</span>1, 1}, {y, <span class="unicode">?</span>1, 1}, Frame <span class="unicode">?</span> False, Axes <span class="unicode">?</span> True]</b><span class="inlinemediaobject"><a NAME="IMG_183"> href="portalcontent.asp?bkid=31099&image_src=https://images.books24x7.com/bookimages/id_31099/fig110%5F02%5F0%2Ejpg&image_id=183&previd=IMG_183"> target="_parent"><img alt="Image from book"> border="0"> height="233"> id="IMG_183"> src="https://images.books24x7.com/bookimages/id_31099/fig110_02.jpg"> title="Click To expand"> width="290"></a></span>

Note that by default the AspectRatio of a ContourPlot will be set to...