Explore quadric surfaces by following the construction steps below.[br][br]Explore the construction and learn how to create quadric surfaces with [i][url=https://www.geogebra.org/3d]GeoGebra 3D Calculator[/url][/i]. Then try it yourself by following the instructions below.

[table][tr][td]1.[/td][td][/td][td]Enter the equation [math]\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1[/math] into the [i]Input Bar [/i]and press [i]Enter[/i]. Sliders for [i]a[/i], [i]b[/i] and [i]c[/i] will be created automatically.[/td][/tr][tr][td]2.[/td][td][/td][td]Drag the sliders to modify the equation. [/td][/tr][tr][td]3.[/td][td][/td][td]Change the equation into the following equations by selecting the equation in the [i]Algebra [i]View[/i][/i], editing it[i] [/i]and pressing [i]Enter[/i]. Discover the changes by moving the sliders.[br][math]\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1,[/math][br][math]\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=1,[/math][br][math]\frac{x^2}{a^2}-\frac{y^2}{b^2}=\frac{z^2}{c^2}[/math][/td][/tr][/table]

If you're using [i]GeoGebra 3D Calculator [/i]on a mobile device you can switch to [i]AR mode[/i] to place your created math objects on any flat surface (e.g. table, floor, ...) around you and walk around them. Explore your constructions from a new perspective!