Ellipse and its properties graph calculator

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F1
F2
P

PF1 = 11
PF2 = 5

PF1 + PF2 = 16

Click P and drag to move the image

An ellipse is the locus of points on a plane where the sum of the distances from a moving point to two fixed points is a constant and this constant is greater than the straight line distance between the two points. It can also be defined as the locus of points where the ratio of the distance to a fixed point to the distance to a fixed line is a constant less than 1. It is a type of conic section, i.e., the section of a cone and a plane. The ellipse plays an important role in Kepler's three laws of planetary motion, i.e., a star is one of the two foci of an ellipse.

You can move the graph up-down, left-right if you hold down the "Shift" key and then drag the graph.

You can use this to investigate the property that Length PF1 + Length PF2 is constant for a particular ellipse. In this example, PF1 + PF2 = 16.