Chapters

## Exercise 1

Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:

1

2

3

4

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## Exercise 2

Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:

## Exercise 3

Determine the equations of the following ellipses using the information given:

,

,

,

,

## Exercise 4

Determine the equation of the ellipse that is centered at (0, 0), passes through the point (2, 1) and whose minor axis is 4.

## Exercise 5

The focal length of an ellipse is 4 and the distance from a point on the ellipse is 2 and 6 units from each foci respectively. Calculate the equation of the ellipse if it is centered at (0, 0).

## Exercise 6

Determine the equation of the ellipse which is centered at (0, 0) and passes through the points:

and .

## Exercise 7

Find the coordinates of the midpoint of the chord in the line: x + 2y − 1 = 0 which intersects the ellipse: x² + 2y² = 3.

## Exercise 8

Determine the equation of the ellipse centered at (0, 0) whose focal length is  and the area of a rectangle in which the ellipse is inscribed within is 80 u².

## Exercise 9

Find the equation of the locus of points P (x, y) whose sum of distances to the fixed points (4, 2) and (−2, 2) is equal to 8.

## Exercise 10

Determine the equation of the ellipse centered at (0, 0) knowing that one of its vertices is 8 units from a focus and 18 from the other.

## Exercise 11

Determine the equation of the ellipse centered at (0, 0) knowing that it passes through the point (0, 4) and its eccentricity is 3/5.

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## Solution of exercise 1

Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:

2

4

## Solution of exercise 2

Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:

1

2

3

4

## Solution of exercise 3

Determine the equations of the following ellipses using the information given:

,        ,

2    ,           ,

3       ,

4     ,

## Solution of exercise 4

Determine the equation of the ellipse that is centered at (0, 0), passes through the point (2, 1) and whose minor axis is 4.

## Solution of exercise 5

The focal length of an ellipse is 4 and the distance from a point on the ellipse is 2 and 6 units from each foci respectively. Calculate the equation of the ellipse if it is centered at (0, 0).

## Solution of exercise 6

Determine the equation of the ellipse which is centered at (0, 0) and passes through the points:

and

## Solution of exercise 7

Find the coordinates of the midpoint of the chord in the line: x + 2y − 1 = 0 which intersects the ellipse: x² + 2y² = 3.

## Solution of exercise 8

Determine the equation of the ellipse centered at (0, 0) whose focal length is  and the area of a rectangle in which the ellipse is inscribed within is 80 u².

## Solution of exercise 9

Find the equation of the locus of points P (x, y) whose sum of distances to the fixed points (4, 2) and (−2, 2) is equal to 8.

## Solution of exercise 10

Determine the equation of the ellipse centered at (0, 0) knowing that one of its vertices is 8 units from a focus and 18 from the other.

## Solution of exercise 11

Determine the equation of the ellipse centered at (0, 0) knowing that it passes through the point (0, 4) and its eccentricity is 3/5.

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