Shown below is a [color=#1e84cc][b]tractrix (pursuit curve) [/b][/color][color=#000000]and a [/color][b]BIG GRAY POINT[/b] [color=#000000]that lies on it. The reflection of this point about the x-axis is also shown (as a much smaller [/color][color=#444444]gray point[/color][color=#000000]). [/color][br][br][color=#ff00ff][b]The pink lines[/b][/color] [color=#000000]are normal to the tractrix. (Recall that a[/color] [b][color=#ff00ff]normal line[/color][/b] [color=#000000]to a curve at a point is the line that is perpendicular to the line tangent to the curve at that point.) [br][/color][br]Drag the [b]BIG GRAY POINT[/b] along this [b]tractrix [/b][color=#000000]and observe this envelope of normal lines (i.e. the traces of the [/color][color=#ff00ff][b]pink lines[/b][/color][color=#000000]). As you do, be sure to keep your finger pressed down on your mouse button as you get closer and closer to the x-axis. (Otherwise, the [/color][b]GRAY POINT[/b][color=#000000] will disappear and you'll have to refresh the page or adjust the slider a bit.) [br][br][/color]What do you see? [color=#000000][br][br]How do your results compare with that from this worksheet? https://tube.geogebra.org/m/FasSGc84[/color]