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# Ellipse (h,k)

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### Ellipse (h,k)

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