The document provides information about ellipses including: 1) An ellipse is defined as the set of all points whose sum of distances from two fixed points (foci) is constant. 2) The general equation of an ellipse with center (h,k) is given as (x-h)2/a2 + (y-k)2/b2 = 1, where a>b>0 and c2 = a2 - b2, with c being the distance from the center to the foci. 3) Examples of specific ellipses are given along with their equations and instructions to graph them.

1. Date: 1.6.12
Title: 10.2 Conics ‐ The Ellipse
Objective: 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
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2. An Ellipse is...
the set of all points (x, y)...the sum of whose distances from
two 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) is
A 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 AM
4x2 + y2 ‐ 8x + 4y + 4 = 0
Parabola? Ellipse? Graph!
Apr 15­2:13 PM
3

4. Ellipse
Find 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