Ellipses in Standard Form

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Show your work for each problem.

1.
What is the center of the ellipse ?
1. a)
2. b)
3. c)
4. d)
2.
Is the ellipse horizontal or vertical?
1. a)Vertical
2. b)Neither
3. c)Horizontal
4. d)Both
3.
For the ellipse , what is the value of ?
4.
For an ellipse with and , find (the distance from center to focus).
5.
What are the vertices of the ellipse ?
1. a)
2. b)
3. c)
4. d)
6.
Find the value of for the ellipse .
7.
Find the foci of the ellipse .
8.
Write the equation in standard form for an ellipse with center , vertices at , and co-vertices at .
9.
The foci of the ellipse are located at:
1. a)
2. b)
3. c)
4. d)
10.
An ellipse has foci at and vertices at . What is ?
11.
Convert to standard form:
12.
Find the equation in standard form for an ellipse with foci at and major axis length of 10.
13.
What is the eccentricity of the ellipse ? Give your answer as a fraction.
14.
Which ellipse has the highest eccentricity?
1. a)
2. b)
3. c)
4. d)
15.
Find all key features of the ellipse : center, vertices, co-vertices, and foci.
16.
For the ellipse , what is the value of ?
17.
Write the equation of an ellipse centered at with (horizontal) and .