Equation of an Ellipse

Equation of an Ellipse in Standard Form

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        where a > 0 and b > 0

The center of this ellipse is ( 0, 0 ).

The extreme points are ( a, 0 ), ( - a, 0 ), ( 0, b ), and (0, - b )

The lines of symmetry are x = 0 and y = 0.

If a = b, then the ellipse is a circle.

If a > b, then the x axis is the major axis.

If a < b, then the y axis is the major axis.

 

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        where a > 0 and b > 0

The center of this ellipse is ( h, k ).

The extreme points are ( h + a, k ), ( h - a, k ), ( h, k + b ), and ( h, k - b )

The lines of symmetry are x = h and y = k.

If a = b, then the ellipse is a circle.

If a > b, then the line y = k is the major axis.

If a < b, then the line x = h is the major axis.