standard form of the equation of an ellipse:

where b^{2}= a^{2} - c^{2}

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 (Â±c,0) (0,Â±c)vertices (Â±a,0) (0,Â±a)covertices (0,Â±b) (Â±b,0)</span>

a is always larger than b; and a,b, and c are related by c^{2}= a^{2} - b^{2}

ex.

Graph 9x^{2}+ 4y^{2}= 36

which is an ellipse.

a^{2} = 9 ; b^{2} = 4

center (0,0)

major axis: y-axis

vertices: (0, Â± 3)

covertices: (Â± 2,0)

Graph 9x^{2 }+ 25y^{2 }= 225

a^{2}= 25 ; b^{2}= 9

center (0,0)

major axis: x-axis

vertices: (Â± 5,0)

covertices (0,Â± 3)

c^{2}= a^{2} - b^{2}

c^{2}= 25 - 9

c^{2} = 16

foci: (Â± 4,0)