Tangents 2

Source code: tangents02    Built with Processing

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This applet displays the curve y=kx² together with two perpendicular tangent lines. Notice that to each tangent line, there is one perpendicular tangent line.

Also notice that the intersection of two perpendicular tangent lines always lies on a particular line. The set of intersection points of all perpendicular tangent lines to a curve is called the isoptic of the curve. For a parabola, the isoptic is a line.

The top slider adjusts the point of tangency while the lower slider adjusts the value of k.