Chapters

## Exercise 1

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

2

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## Exercise 2

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

## 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

3

Divide by 30:

4

Divide by 1296:

## Solution of exercise 2

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

1

2

## 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 / .

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## 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.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.