Description of the Construction[br][br]The Lemniscate of Bernoulli is a degree-four curve shaped like a sideways figure-eight (∞). It is defined as the locus of all points P such that the product of the distances to two fixed points (the foci)[br]F₁ and F₂ is constant:[br]PF₁ × PF₂ = c²[br][br]Construction Overview:[br]1. Two foci F₁ and F₂ are placed on the x-axis.[br]2. The midpoint O of the foci defines the center of symmetry of the lemniscate.[br]3. The distance between the foci is 2c, and the constant of the locus is c².[br]4. The lemniscate is drawn using the Cartesian equation:[br](x² + y²)² = 2c²(x² − y²)[br]5. A test point P is placed on the curve, and GeoGebra dynamically computes both PF₁ × PF₂ and c² for comparison.[br][br]Drag Test[br]• Drag the foci F₁ or F₂ along the x-axis. The curve resizes but keeps its shape (the product property still holds).[br]• Move the point P around the lemniscate. The computed product PF₁ × PF₂ stays constant and equal to c².[br]• The red circle centered at O with radius √2c provides a visual reference for the outer boundary.[br][br]This drag test allows you to confirm dynamically that the lemniscate maintains its geometric relationship for all positions of P and for any adjustment of the foci.