Section 10.2 ellipse

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  • 1. Date:  1.6.12Title:  10.2 Conics ‐ The EllipseObjective: To create Ellipses!In: Feb 5­7:22 PM Remember Circles? x2 + y2 = r2 (x + 3)2 + (y - 2 )2 = 16 Really, a Circle formula should read.... (x-h)2 + (y-k)2 = 1 r2 r2 Apr 15­2:13 PM 1
  • 2. An Ellipse is...the set of all points (x, y)...the sum of whose distances fromtwo distinct fixed points (foci) is constant.Eccentricity is the ratio c/a Apr 15­2:13 PM Ellipse An equation of the ellipse with center (0, 0) and foci at (-c, 0) and (c, 0) isA equation of the ellipse with center (h, k),changes to the following: where a > b > 0 and c2 = a2 ‐ b2 C is the distance from the center to the foci points. (a is always the bigger number) Apr 15­2:13 PM 2
  • 3. Graph: 4x2 + y2 + 24x ­ 4 y + 24 = 0 HW: P 710   12,15,17,18,20,22,30,32,33,40,48,49 Nov 30­8:04 AM4x2 + y2 ‐ 8x + 4y + 4 = 0Parabola?  Ellipse?  Graph! Apr 15­2:13 PM 3
  • 4. EllipseFind an equation of the ellipse with center at the origin,  one focus at (3, 0), and a vertex at (‐4, 0). Graph the ellipse by hand Apr 15­2:13 PM Ellipse How will the graphs look different? x2 + y2 = 1 x2 + y2 = 1 25 9 9 25 Apr 15­2:13 PM 4
  • 5. Ellipse Find an equation of the ellipse having one focus at (0, 2) and vertices at (0, ‐3) and (0, 3).   Apr 15­2:13 PM 5