Small practice
brighter futures.
Checking sign-in status
Menu

Conic sections practice

Properties of hyperbolas worksheets

Find exact vertices, foci and opening directions from horizontal and vertical standard-form hyperbola equations.

Ready-made English PDF · fixed settings

Worksheet · LetterWorksheet · A4
Customize worksheet ↓
With answer key

Customization below makes a separate PDF.

First page of the properties of hyperbolas worksheets printable worksheetOpen full-size sample (first page)

Fixed English ready-made files. Custom settings below apply only to the configured PDF.

Ready to print

Start with a ready-made worksheet

Identify the requested exact properties of each hyperbola.

Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.

US Letter

Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
Customize this worksheet

Paper sizes and printing help · More conic sections activities

Read the transverse direction and exact focal distance

Each worksheet contains eight horizontal and vertical hyperbolas. Choose vertices, foci, opening directions or any combination.

The positive term identifies the transverse axis, and c² = a² + b² gives the focal distance.

The separate key supplies only the selected exact properties.

Learning objective

What this activity builds

Derive exact geometric properties from an axis-aligned hyperbola in standard form.

Worked example

Find the foci of x²/9 − y²/16 = 1.

(−5, 0) and (5, 0).

For a hyperbola c² = a² + b², so c² = 9 + 16 = 25.

Teaching notes

Make the practice count

  • The positive squared term identifies the transverse direction.
  • Use c² = a² + b² for the focal distance.
  • Keep translated radical coordinates exact.
  • Equal denominators still define a valid rectangular hyperbola.

Make it yours

Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose one or more exact properties, then change the seed for eight reproducible horizontal and vertical hyperbolas.

Worksheet settings

Properties
Page note and reproducible seed

The same settings and seed make the same questions. Shared links include your page note; leave personal information out. Notes use the selected language’s supported characters; English accepts basic Latin text.

Configured PDF · Properties of Hyperbolas · US Letter

Preview ready. Download includes these exact pages.

2 student pages
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScore/ 24TeacherDateProperties of HyperbolasIdentify the requested exact properties of each hyperbola.1.x-52100-1·y-82100=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________2.y+52144-1·x+121=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________3.x+1236-1·y-529=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________4.y+3225-1·x+8249=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________5.x-22144-1·y+4281=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________6.y-3249-1·x-724=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________7.x-229-1·y-7249=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________math-sheet.comPage 1 / 2
Math SheetNameScore/ 24TeacherDateProperties of HyperbolasIdentify the requested exact properties of each hyperbola.8.y+8216-1·x+5264=1Vertices: ______________________________Foci: ______________________________Opens: ______________________________math-sheet.comPage 2 / 2

A useful next step

Related activities

First page preview: Graphing hyperbolas worksheets

Conic sections

Graphing hyperbolas worksheets

Graph both visible branches, vertices, construction rectangles and asymptotes on equal-scale coordinate grids.

Preview and download
First page preview: Properties of ellipses worksheets

Conic sections

Properties of ellipses worksheets

Find exact centers, vertices, co-vertices, foci, axis lengths and eccentricity from standard-form ellipse equations.

Preview and download