Ellipse Problems

1Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:

1 Ellipse Problem

2 Ellipse Problem

3 Ellipse Problem

4 Ellipse Problem

2Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:

1 Ellipse Problem

2 Ellipse Problem

3 Ellipse Problem

4 Ellipse Problem

3Determine the equations of the following ellipses using the information given:

1 Ellipse Problem

2 Ellipse Problem

3 Ellipse Problem

4 Ellipse Problem

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

5The 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).

6Determine the equation of the ellipse which is centered at (0, 0) and passes through the points:Ellipse Problem.

7Find the coordinates of the midpoint of the chord in the line: x + 2y − 1 = 0 which intersects the ellipse: x2 + 2y2 = 3.

8Determine the equation of the ellipse centered at (0, 0) whose focal length is número and the area of a rectangle in which the ellipse is inscribed within is 80 u2.

9Find 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.

10Determine 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.

11Determine the equation of the ellipse centered at (0, 0) knowing that it passes through the point (0, 4) and its eccentricity is 3/5.

 

1

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

1 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution

Elements of an Ellipse

2 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Ellipse

3 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Vertical Major Axis Ellipse

4 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Ellipse

 

2

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

1 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Ellipse

2 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Vertical Major Axis Ellipse

3 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Horizontal Major Axis Ellipse

4 Ellipse Exercises

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution

Ellipse Solution


Ellipse

3

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

1 Ellipse Exercises

Ellipse Operations

Ellipse Solution


2 Ellipse Exercises

Ellipse Operations

Ellipse Solution


3 Ellipse Exercises

Ellipse Operations

Ellipse Solution


4 Ellipse Exercises

Ellipse Operations

Ellipse Solution

 

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.

formulas

Ellipse Operations

Ellipse Solution

 

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).

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution

 

6

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

Ellipse Operations

Ellipse Solution

 

7

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

 

Ellipse-Line Intersection

Ellipse Operations

Ellipse Operations

Ellipse Solution

 

8

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

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution

 

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.

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution

 

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.

Ellipse Exercises

Ellipse Operations

Ellipse Operations

Ellipse Solution

 

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.

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution

 



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