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Ellipse (h,k)

This document discusses the standard forms of ellipses and provides formulas for the coefficients, length of latus rectum, and eccentricity. It also gives examples of finding the equation of an ellipse given properties like the foci, vertex, endpoints of the minor axis, and eccentricity.

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Standard Form of Ellipse Case 1: Ellipse with center at (h,k) and the major axis is parallel to the x-axis.
Standard Form of Ellipse Case 2: Ellipse with center at (h,k) and the major axis is parallel to the y-axis
Other important formulae to remember Relationship between the coefficients a , b , and c in an ellipse
Other important formulae to remember Length of each latus rectum ( latera recta , plural )
Other important formulae to remember Eccentricity of ellipse
Find the equation of the ellipse with vertex at (4,3), and foci at (-3,3) and (3,3). ILLUSTRATIVE EXAMPLE:
Find the equation of the ellipse with vertex at (5,2), and foci at (-4,2) and (4,2). ILLUSTRATIVE EXAMPLE:
Find the equation of the ellipse with endpoints of the minor axis (-1,3) and (-1,-1) and a focus at (1,1) ILLUSTRATIVE EXAMPLE:
Find the equation of the ellipse with foci at (2,3) and (2,-1) and an endpoint of minor axis at (4,1). ILLUSTRATIVE EXAMPLE:
ILLUSTRATIVE EXAMPLE: Find the equation of the ellipse with vertices at (-2,1) and (4,1) with eccentricity of 2/3.
ILLUSTRATIVE EXAMPLE: Find the equation of the ellipse with center at (-2,2), vertex at (-2,4) and a focus at (-2,3)