NOTE: We are going to use the section formula to derive the equation of ellipse. Since there are 2 variants of the formula (external and internal division), we get 2 foci and 2 directrices.
An ellipse is a conic section, whose eccentricity is less than 1. In other words, if is a focus and is the directrix, then for any point ,
The standard equation of ellipse is
 Ellipse is horizontal, when i.e. more stretched in direction, vertical, when
 Closed curve
 Symmetric about and axes
 Does not pass through the origin
 Intersection with axis – at and
 Intersection with axis – at and
 Foci : and , directrices :
 Sum of focal distances = = constant (We’ve used this as the condition for locus of a point)
 Length of latus rectum =
 Parametric Equations :

Where can you find the elliptic shape?
I) Earth’s orbit around Sun, with Sun as one of the foci of the ellipse
II) The rugby ball
III) Batman logo (boundary)
IV) Eggs, lemons
V) Whispering galleries
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