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
1

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