Name: Parabola Problems
Brand: Superprof
SKU: SP-RB-00004416
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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

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Exercise 1

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

1 $\text{[math]}$

2 $\text{[math]}$

3 $\text{[math]}$

4 $\text{[math]}$

Exercise 2

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

1 $\text{[math]}$

2 $\text{[math]}$

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: $\text{[math]}$ and $\text{[math]}$ . .

Exercise 7

Determine the equation of the hyperbola centered at (0, 0) that passes through the point $\text{[math]}$ and whose eccentricity is $\text{[math]}$ .

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 $\text{[math]}$ .

Exercise 10

A rectangular hyperbola passes through the point $\text{[math]}$ . 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 $\text{[math]}$ . Calculate the equation of this hyperbola.

Exercise 12

Calculate the equation of a rectangular hyperbola knowing that its focal length is $\text{[math]}$ .

Exercise 13

The length of the conjugate axis of a hyperbola is 8 and the equations of the asymptotes are: $\text{[math]}$ . . 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 $\text{[math]}$

Determine and plot the coordinates of the foci and vertices

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

2 $\text{[math]}$

Determine and plot the coordinates of the foci and vertices

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

3 $\text{[math]}$

Divide by 30:

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

4 $\text{[math]}$

Divide by 1296

Divide by 1296:

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

Solution of exercise 2

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

1 $\text{[math]}$

exercise solutions

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

2 $\text{[math]}$

exercise solutions

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

Solution of exercise 3

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

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

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.

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

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.

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

Solution of exercise 6

Determine the equation of the hyperbola centered at (0, 0) that passes through the points: $\text{[math]}$ and $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 7

Determine the equation of the hyperbola centered at (0, 0) that passes through the point $\text{[math]}$ and whose eccentricity is $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

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.

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

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.

exercise solutions

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

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.

exercise solutions

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$

Solution of exercise 11

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

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 12

Calculate the equation of a rectangular hyperbola knowing that its focal length is $\text{[math]}$ / .

$\text{[math]}$ $\text{[math]}$

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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: $\text{[math]}$ . Calculate the equation of the hyperbola, its foci and vertices.

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$

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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.

Hyperbola Problems

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

Theory

Equation of a Circle

Hyperbola

Equation of the Hyperbola

Eccentricity of a Hyperbola

Conics

Parabola

Equation of a Parabola

Rectangular Hyperbola

Ellipse

Circle-Line Intersection

Eccentricity of the Ellipse

Equation of an Ellipse

Formulas

Hyperbola Formulas

Parabola Formulas

Ellipse Formulas

Circle Equation Formulas

Exercises

Equation of a Circle Problems

Ellipse Problems

Hyperbola Problems

Parabola Problems

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