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Ellipses (section 11-4)

Ellipses (section 11-4). Ellipse:. The set of all points such that the sum of the distances from a point on the ellipse to two fixed points is constant. P. The points are called foci singular: focus. PF 1 and PF 2 are called focal radii. F 1. F 2.

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Ellipses (section 11-4)

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  1. Ellipses(section 11-4)

  2. Ellipse: The set of all points such that the sum of the distances from a point on the ellipse to two fixed points is constant. P The points are called foci singular: focus PF1 and PF2 are called focal radii F1 F2

  3. The center is the midpoint of the line segment joining the foci The chord passing through the foci is the major axis The chord passing through the center and perpendicular to the major axis is the minor axis F1 F2 C

  4. y b x a -c c The equation of an ellipse: (horizontal) Where: center (h, k) sum of focal radii = 2a foci (-c, 0), (c, 0) b2 = a2 – c2

  5. y (0,b) x (-c,0) (c,0) (a,0) Derive: b2 = a2 – c2 B F1 F2

  6. y a c x b -c The equation of an ellipse: (vertical) Notice:a2 > b2 or c2 when: a2 is denom of “y” term → vertical when: a2 is denom of “x” term → horizontal Where: center (h, k) sum of focal radii = 2a foci (0, -c), (0, c) b2 = a2 – c2

  7. Ex. 1: Give the x- and y-intercepts, find the foci, and graph the ellipse 9x2 + 4y2 = 144: (rewrite in correct form)

  8. Ex. 2: Find the foci and graph the ellipse x2 + 4y2 – 16 = 0:

  9. Ex. 3: Find the foci and graph the ellipse:

  10. Ex. 4: Find an equation for the ellipse having x-intercepts 2 and y-intercepts :

  11. Ex. 5: Find an equation for the ellipse having foci at (0, -3) and (0, 3) and sum of focal radii equal to 10:

  12. Ex 6: Find the center and foci of the ellipse (sketch) •

  13. Ex 7: Find the center and foci of the ellipse (sketch) •

  14. Homework:Day 1: pg. 736 #9-27 odds (use graph paper)Day 2: worksheet (ellipse) #1-10

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