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An interactive three dimensional plot with axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\text{.}\) A slider at the top of the figure allows the user to change the value of k and a checkbox allows a grid of vectors to be drawn along the surface. The value of k changes the shape of the surface plotted in light blue. For negative values of k, a hyperboloid of two sheets is drawn with smaller values of k having a larger gap between the two sheets. For k equal to zero, a cone centered along the z-axis is shown. For k greater than zero, a hyperboloid of one sheet is shown with larger values of k having a larger opening around the z-axis. The vectors drawn are perpendicular to the surface at the point they are drawn and point away from the z-axis.