In this activity, you will explore the properties of tangents to an ellipse using an interactive construction:[list=1][*]Ellipse and Foci: Two points, F1 and F2, define the foci of the ellipse, and a slider sets the semi-major axis [code]a[/code].[br][/*][*]Draggable Point (P): A point [code]P[/code] lies on the ellipse and can be dragged along its curve.[br][/*][*]Tangent Line at P: The tangent line at [code]P[/code] updates dynamically as [code]P[/code] moves.[br][/*][*]Drag Test with Point Q:[list][*]You can drag a free point [code]Q[/code].[br][/*][*]The activity checks whether [code]Q[/code] lies on the tangent at [code]P[/code].[br][/*][/list][/*][*]Explore: Drag [code]P[/code] to see the tangent move and experiment with placing [code]Q[/code] to understand how points relate to the tangent line.[/*][/list]