The Ellipse. Analytic Geometry Section 3.3. Definition of “ellipse”. An ellipse is the set of all points in a plane such that the distance from two fixed points (foci) on the plane is a constant. The equation of an ellipse with its center at the origin has one of two forms:.
The position of the a2 (under the x or y) tells you whether the horizontal or the vertical axis is the major axis of the ellipse.Equation of the Ellipse
The ends of the minor axis are at (0,b) and (0,-b).
The foci are at (c,0) and (-c,0).The Ellipse
The endpoints of the two latus recti are found using the equivalence :
Relating these values to the standard form for an ellipse whose center is at the origin and whose major axis is horizontal, ,
and the equivalence
applies. Solve for b2 to get
In this case,
3.3: 2, 3, 15, 16, 17, 22, 25, 44