Ellipse Notes
What is an ellipse?
• The set of all points, P, in a plane such that the sum of the distances between P and the foci is constant.
12
2
2
2
bky
ahx
12
2
2
2
bky
ahx
h and k give the x and y values of the center.Take the opposite of h and k so the center is (-h, -k)
The square root of the number under x tells you how far to move horizontally.
The square root of the number under y tells you how far to move vertically.
A and B can switch places. A goes under the MAJOR axis. B goes under the MINOR axis.
14
336
2 22
yx
Center
Major Axis
Minor Axis
a
b
(2, 3)
X, horizontal
Y, vertical
6
2
-5 10
-2
8
x
y
Foci (plural of focus)
Center
Major Axis
Minor Axis
a
b
(2, 3)
X, horizontal
Y, vertical
7
4
149
316
2 22
yx
-3 7
-5
11
x
y
The Focus Equation: • The focus, c, is used as a tool for finding the
vertex or co-vertex. *
• You will not be graphing the focus.
• You will only use the focus, c, if you are writing equations
Center
Major Axis
Minor Axis
a
b
(3, -1)
X, horizontal
Y, vertical
5
4
125
116
3 22
yx
-10 10
-10
10
x
y
Center
Major Axis
Minor Axis
a
b
(-1, 2)
X, horizontal
Y, vertical
7
2
-10 10
-10
10
x
y
14
249
1 22
yx
Center
Major Axis
Minor Axis
a
b
(-5, 3)
X, horizontal
Y, vertical
5
2
-10
-5
10
x
y
125
345 22
yx
Center
Major Axis
Minor Axis
a
b
(3, -1)
X, horizontal
Y, vertical
4
3
19
116
3 22
yx
-5 10
-5
5
x
y