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