September 24, 2020

Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Exercise 12
- Exercise 13
- 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
- Solution of exercise 12
- Solution of exercise 13

## Exercise 1

Determine and plot the coordinates of the foci and vertices and calculate the eccentricity of the following hyperbolas:

1

2

3

4

## Exercise 2

Determine and plot the coordinates of the foci and vertices and calculate the eccentricity of the following hyperbolas:

1

2

## Exercise 3

Calculate the equation of the hyperbola with a transverse axis of 8 and a focal length of 10.

## Exercise 4

The transverse axis of a hyperbola is 12 and the curve passes through the point P = (8, 14). Find its equation.

## Exercise 5

Calculate the equation of the hyperbola centered at (0, 0) whose focal length is 34 and the distance from one focus to the closest vertex is 2.

## Exercise 6

Determine the equation of the hyperbola centered at (0, 0) that passes through the points: and . .

## Exercise 7

Determine the equation of the hyperbola centered at (0, 0) that passes through the point and whose eccentricity is .

## Exercise 8

Determine the equation of the hyperbola centered at (0, 0) knowing that one focus is 2 units from one vertex and 50 from the other.

## Exercise 9

Determine the coordinates of the point(s) of intersection between the line x + y − 1 = 0 and the hyperbola .

## Exercise 10

A rectangular hyperbola passes through the point . Find its equation and determine the coordinates of the vertices and foci.

## Exercise 11

The transverse axis of a hyperbola is 12 and the eccentricity is . Calculate the equation of this hyperbola.

## Exercise 12

Calculate the equation of a rectangular hyperbola knowing that its focal length is .

## Exercise 13

The length of the conjugate axis of a hyperbola is 8 and the equations of the asymptotes are: . . Calculate the equation of the hyperbola, its foci and vertices.

## Solution of exercise 1

Determine and plot the coordinates of the foci and vertices and calculate the eccentricity of the following hyperbolas:

1

2

3

Divide by 30:

4

Divide by 1296:

## Solution of exercise 2

1

## Solution of exercise 3

Calculate the equation of the hyperbola with a transverse axis of 8 and a focal length of 10.

## Solution of exercise 4

The transverse axis of a hyperbola is 12 and the curve passes through the point P = (8, 14). Find its equation.

## Solution of exercise 5

Calculate the equation of the hyperbola centered at (0, 0) whose focal length is 34 and the distance from one focus to the closest vertex is 2.

## Solution of exercise 6

Determine the equation of the hyperbola centered at (0, 0) that passes through the points: and .

## Solution of exercise 7

Determine the equation of the hyperbola centered at (0, 0) that passes through the point and whose eccentricity is .

## Solution of exercise 8

Determine the equation of the hyperbola centered at (0, 0) knowing that one focus is 2 units from one vertex and 50 from the other.

## Solution of exercise 9

Determine the coordinates of the point(s) of intersection between the line x + y − 1 = 0 and the hyperbola x² - 2y²= 1.

## Solution of exercise 10

A rectangular hyperbola passes through the point (4, 1/2). Find its equation and determine the coordinates of the vertices and foci.

## Solution of exercise 11

The transverse axis of a hyperbola is 12 and the eccentricity is 4/3. Calculate the equation of this hyperbola.

## Solution of exercise 12

Calculate the equation of a rectangular hyperbola knowing that its focal length is / .

## Solution of exercise 13

The length of the conjugate axis of a hyperbola is 8 and the equations of the asymptotes are: . Calculate the equation of the hyperbola, its foci and vertices.

Thanks,the exercises are really of help.