Create an ellipse with the intersection point of two tangents and animate the construction by following the construction steps below.

[b]Note:[/b] If you're using the Mobile App make sure that the chosen [i]Labeling[/i] option is [i]New Points Only[/i]. You can change this by going to the [i]Settings [/i]in the app's menu and then selecting [i]General.[/i][br][br][table][tr][td]1.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_ellipse3.png[/icon][/td][td]Create an ellipse using the [i]Ellipse[/i] tool.[/td][/tr][tr][td]2.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/td][td]With the [i]Line[/i] tool select point [i]A[/i] and create a point [i]D[/i] on the outline of the ellipse.[/td][/tr][tr][td]3.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_point.png[/icon][/td][td]Create point [i]E [/i]by selecting the second intersection point of the created line and the outline of the ellipse.[/td][/tr][tr][td]4.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_tangent.png[/icon][/td][td]Select the [i]Tangents[/i] tool to create the tangents of the ellipse at point [i]D[/i] and [i]E[/i].[br]For the first tangent select the point [i]D[/i] and then the outline of the ellipse. Repeat this for the second tangent with point [i]E[/i].[/td][/tr][tr][td]5.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Create the intersection point [i]F[/i] of the two tangents using the [i]Intersect[/i] tool.[/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Change the color of point [i]F[/i] to red.[/td][/tr][tr][td]7.[/td][td] [/td][td]Move point [i]D.[/i][br][b]Note: [/b]When using the Online or Desktop App you can animate point [i]D [/i]by selecting it and[i] [/i]then choosing [i]Animation.[/i][/td][/tr][/table][b][br]Note:[/b] Open the context menu of point [i]F[/i] by selecting the [i]More [/i]button and activate [i]Show[/i] [i]Trace[/i]. Then move point [i]D[/i] again to be able to observe the trace of point [i]F[/i].[br]