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Ellipses

Ellipses. Section 8.2. Ellipse. Set of all points whose distance from TWO f ixed points have a constant sum. Major Axis (long one) Minor Axis (short one) Center: (h, k). a > b. Major Axis - X. a. a. VERTEX. VERTEX. c. c. b. FOCUS. FOCUS. Major Axis - Y. c. b. a.

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Ellipses

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  1. Ellipses Section 8.2

  2. Ellipse Set of all points whose distance from TWO fixed points have a constant sum

  3. Major Axis (long one) • Minor Axis (short one) • Center: (h, k) a > b

  4. Major Axis - X a a VERTEX VERTEX

  5. c c b FOCUS FOCUS

  6. Major Axis - Y c b a

  7. 1. Graph Center: ________ a = ______ b = ______ c2 = ______ c = ______ Vertices: ________ & _______ Foci:________ & ________

  8. 1. Graph Center: ________ a = ______ b = ______ c2 = ______ c = ______ Vertices: ________ & _______ Foci:________ & ________

  9. 3. Find the standard form of the equation for an ellipse whose major axis has endpoints (0, 6) and (0, -6), and minor axis length 8.

  10. Eccentricity The “ovalness” of an ellipse e = 0 e = 0.02 e = 0.87

  11. Changing to Standard Form • Moveconstant to one side • Group x-terms and y-terms • Take out GCF (if there is one) • Complete the square (keep things balanced!) • Factor • Divide by constant

  12. 1. x2 + 5y2– 8x – 30y – 39 = 0

  13. 2. x2 + 4y2 + 8x – 8y + 16 = 0

  14. 2. 9x2 + 4y2 + 126x + 64y + 661 = 0

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