Move the foci F_{1} and F_{2} that define the position of the focal axis of the conic, set the length of the major axis of the conic using the Maxis slider, then move point P along the circle to view the locus.
To reproduce the construction:

Draw the circle with center F_{1} and radius r = Maxis

Create a point P on the circle, then draw the perpendicular bisector of segment PF_{2}

Line PF_{1 }intersects the perpendicular bisector at a point L, which is a point of the conic

Point P, moving on the circle, creates the locus of points L, that is:
- an ellipse if F_{2} is inside the circle distance between foci < axis length → e < 1
- an hyperbola if F_{2 }is outside the circle distance between foci > axis length → e > 1
- a circle if F_{1} ≡ F_{2} distance between foci = 0 → e = 0
(e = eccentricity)

Explore the locus

After creating the locus, draw triangle PLF_{2}.

What type of triangle is it? Explain.

Write the canonical definition (as locus) of the conic that you see in the construction.

Use the properties of triangle PLF_{2} to show that the graph in the construction matches the canonical definition.