Introduction to Ellipses

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Show your work for each problem.

1.
What shape is an ellipse most similar to?
1. a)A triangle
2. b)A square
3. c)A straight line
4. d)A stretched circle
2.
In the equation , what is ?
1. a)3
2. b)16
3. c)4
4. d)9
3.
For the ellipse , what is the value of ?
4.
The formula for finding the distance from the center to each focus is:
1. a)
2. b)
3. c)
4. d)
5.
If and , calculate .
6.
For the ellipse , the major axis is:
1. a)Circular
2. b)Diagonal
3. c)Horizontal
4. d)Vertical
7.
Find the foci of the ellipse .
8.
What is the center of the ellipse ? Enter as (x, y).
9.
Find all vertices of the ellipse .
10.
Which equation represents a vertical ellipse?
1. a)
2. b)
3. c)
4. d)
11.
For the ellipse , what is the length of the major axis?
12.
Write the equation of an ellipse centered at the origin with vertices at and co-vertices at .
13.
For the ellipse , find the distance between the two foci.
14.
Find all key features of the ellipse : center, vertices, co-vertices, and foci.
15.
An ellipse has foci at and vertices at . What is ?
1. a)2
2. b)4
3. c)8
4. d)16
16.
Write the equation of an ellipse centered at with a vertical major axis of length 12 and a minor axis of length 8.
17.
What happens to the foci when an ellipse becomes a circle?
1. a)They disappear completely
2. b)They move outside the curve
3. c)They become infinitely far apart
4. d)They merge into a single point (the center)