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Conic Sections - Ellipse

standard form of the equation of an ellipse:

where b2= a2 - c2

center (0,0) (0,0)major axis on x-axis, length 2a on y-axis, length 2aminor axis on y-axis, length 2b on x-axis, length 2bfoci (±c,0) (0,±c)vertices (±a,0) (0,±a)covertices (0,±b) (±b,0)</span>

a is always larger than b; and a,b, and c are related by c2= a2 - b2

ex.
Graph 9x2+ 4y2= 36

which is an ellipse.
a2 = 9 ; b2 = 4
center (0,0)
major axis: y-axis
vertices: (0, ± 3)
covertices: (± 2,0)

Graph 9x2 + 25y2 = 225

a2= 25 ; b2= 9
center (0,0)
major axis: x-axis
vertices: (± 5,0)
covertices (0,± 3)

c2= a2 - b2
c2= 25 - 9
c2 = 16

foci: (± 4,0)

Subject: 
Algebra
Subject X2: 
Algebra

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