Name: Parabola Problems and Worked Solutions
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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.

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One piece

September 2024

There are errors with the answers. The 2y was squared during the substitutions, similar things occuring throughout the examples

Viktor

September 2024

In my opinion there are mistakes while substituting “y” into circle formula.

Daisy

September 2023

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.

Sallu Gerald KaiKai

March 2022

It is clear and understandable .

jay

September 2021

thankyouuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu

Mary Wasai

December 2020

This is very nice but please show how to find the 4p

Enabel

March 2025

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

Vanessa

April 2025

Hi Enabel! Thanks for sharing this helpful advice!

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

Eccentricity of the Ellipse

Equation of an Ellipse

Solving Circle-Line Intersection Problems

Formulas

Hyperbola Formulas

Parabola Formulas

Ellipse Formulas

Circle Equation Formulas

Exercises

Equation of a Circle Problems

Ellipse Problems

Hyperbola Problems

Parabola Problems and Worked Solutions

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