Second-order implicit equation locus

Vary the sliders to adjust the coefficients in the general second-order implicit equation. Use the input area at the bottom to enter specific values, e.g., a=5, then b=0, then c=-4, and so on. Be sure to define all six coefficients, including any that are zero. The area at the left displays a variety of information about the function. Hover the mouse over these entries for more information. If the roots are real they are shown on the x-axis; the y-intercepts are also shown if they exist. It is interesting to see how these four points move, or don't move, as the coefficients are varied.. 

NOTE:The labeling of the locus may not be correct for some degenerate cases. 

Use the zoom tool to adjust the range of the axes (the tool has a black icon which may be difficult to see on the black background.) The tool with the double arrows allows shifting the entire plot range; it moves the graphic left/right/up/down within the window.When done with zoom or movement, click the arrow icon at left on the toolbar to re-enable control of the sliders with the mouse.

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WCEvans (9/09), Created with GeoGebra