Ellipses and Circles

Locus

loc

a locus (plural: loci) is a set of points whose location satisfies or is determined by one or more specified conditions.

A locust eats plants.

Drag the foci or the point on the ellipse. The ellipse is defined by all points P such that PF₁ + PF₂ = constant.

F₁ = (, )

F₂ = (, )

P = (, )

PF₁ + PF₂ =

Ellipse equation (standard form):
(x − h)² / a² + (y − k)² / b² = 1

h = , k = , a = , b = , c =

Ellipse

An ellipse is the set of points drawn out when the sum of the distances of two fixed points, the focii , are constant for any point.

ani

An ellipse with centre ( 0 , 0 ) has equation

Example

Draw the ellipse defined by the equation

Solution

ani2