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An Ellipse is the set of all points in a plane,whose distances from a fixed point in the plane and their distances from a fixed line in the plane bear a constant ratio,less than 1. The fixed point is calledThe two fixed points are called the foci (plural of ‘focus’) of the ellipse.

The mid point of the line segment joining the foci is called the center of the ellipse. The line segment through the foci of the ellipse is called the major axis and the line segment through the center and perpendicular to the major axis is called the minor axis. The end points of the major axis are called the vertices of the ellipse.

The eccentricity of an ellipse is the ratio of the distances from the center of the ellipse to one of the foci and to one of the vertices of the ellipse (eccentricity is denoted by e) e = c / a

Standard equations of an ellipse The equation of an ellipse is simplest if the center of the ellipse is at the

if

If

Center is other than origin :

If the coordinates of center (h,k) then the equation of ellipse is

Here , center ( 2,3 ) and a= 3 and b = 2 so a > b .

∴ Ellipse main axis is X-axis.( Horizontal Ellipse)

Here, center ( -2, -3 ) and a = 2 and b = 4 so a< b

∴ Ellipse main axis is Y- axis. (Vertical Ellipse).

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