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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
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
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
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