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The standard equation of ellipse is used to represent a general ellipse algebraically in its standard form. The standard equations of an ellipse are given as, x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , for the ellipse having the transverse axis as the x-axis and the conjugate axis as the y-axis.
The conic equation of an ellipse is x2/a2 + y2/b2 = 1, and the equation of the auxiliary circle is x2 + y2 = a2.
For an ellipse having the standard equation x2a2+y2b2 x 2 a 2 + y 2 b 2 = 1, the vertices of ellipse are (+a, 0), (-a, 0), the length of the major axis is 2a, and the center of the ellipse is (0, 0).
The standard equation for this ellipse is ( x ? h ) 2 a 2 + ( y ? k ) 2 b 2 = 1 . The center is , the major axis is 14 units long, making , and the minor axis is 6 units long, making .
The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. ?In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.