Chapters
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9
- Solution of exercise 10
- Solution of exercise 11
Exercise 1
Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:
1 
2 
3 
4 
Exercise 2
Calculate and plot the coordinates of the foci and vertices and determine the eccentricity of the following ellipses:
1 
2 
3 
4 
Exercise 3
Determine the equations of the following ellipses using the information given:
1 
, 
2 , 
3 
, 
4 
, 
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:
1
2
3 
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:
1 , ,
2 , ,
, 
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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There are errors with the answers. The 2y was squared during the substitutions, similar things occuring throughout the examples
In my opinion there are mistakes while substituting “y” into circle formula.
Am I going mad, or are all of the workings on the circle/line intersection examples wrong? Eg Example 4 there is a term of 5x missing in step 2.
It is clear and understandable .
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This is very nice but please show how to find the 4p
It’s already been in the formula, but if you reffering why the 4p was used in the formula try take chat with deepseek, it was a good gpt alternatives even better for math
Hi Enabel! Thanks for sharing this helpful advice!