Small practice
brighter futures.
Checking sign-in status
Menu

Conic sections practice

Classifying conic sections worksheets

Classify circles, ellipses, parabolas and hyperbolas from standard or general equations, then convert and graph general 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 classifying conic sections 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

Classify each conic, then complete the requested standard-form and graph work.

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

Classify, convert and graph all four conic families

The worksheet keeps all sixteen source-backed exercises: six classification questions, six general-to-standard conversions and four general equations to classify, convert, graph and analyze.

The equation-form control applies only to the first section. The conversion and graph sections always begin with general equations.

The separate key identifies each conic and supplies exact standard forms, graphs and requested features.

Learning objective

What this activity builds

Use exact coefficients and completed-square forms to identify and represent all four axis-aligned conic families.

Worked example

Classify 9x² + 4y² − 36 = 0.

Ellipse: x²/4 + y²/9 = 1.

Both squared coefficients normalize to positive values, but their denominators differ.

Teaching notes

Make the practice count

  • One squared variable indicates a parabola.
  • Equal positive squared terms indicate a circle.
  • Unequal positive terms indicate an ellipse.
  • Opposite signs on squared terms indicate a hyperbola.

Make it yours

Customize the practice

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

Choose conic types and the equation form for the first six classification questions. Conversion and graph sections always start with general equations.

Worksheet settings

Conic types

This choice applies to the first six classification questions. Conversion and graph questions always start in general form.

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 · Classifying Conic Sections · US Letter

Preview ready. Download includes these exact pages.

4 student pages
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScore/ 16TeacherDateClassifying Conic SectionsClassify each equation. The selected equation mode applies to this section.1.x-529+y+2236=1Type: ____________________2.x-52+y-42=36Type: ____________________3.y=6·x+32+2Type: ____________________4.y-229-1·x-1236=1Type: ____________________5.x+3225+y-4216=1Type: ____________________6.x+52+y+42=25Type: ____________________math-sheet.comPage 1 / 4
Math SheetNameScore/ 16TeacherDateClassifying Conic SectionsClassify each general equation and write it in standard form.7.-12·x2-3·y2+72·x+24·y-144=0Type: ____________ Standard form:8.-1·x2-1·y2+6·x+6·y-2=0Type: ____________ Standard form:9.-32·x2+2·y2+192·x-8·y-248=0Type: ____________ Standard form:10.6·y2+2·x-24·y+32=0Type: ____________ Standard form:11.-72·x2-50·y2-288·x-200·y+1312=0Type: ____________ Standard form:12.2·x2+2·y2-50=0Type: ____________ Standard form:math-sheet.comPage 2 / 4
Math SheetNameScore/ 16TeacherDateClassifying Conic SectionsClassify, write standard form, graph and give the named features. Each grid square is 1 unit.13.50·x2+8·y2-200·x-32·y+32=0Each square = 1 unitStandard form:Type: ____________________Center:Vertices:Foci:14.4·y2-1·x+8·y+3=0Each square = 1 unitStandard form:Type: ____________________Vertex:Focus:math-sheet.comPage 3 / 4
Math SheetNameScore/ 16TeacherDateClassifying Conic SectionsClassify, write standard form, graph and give the named features. Each grid square is 1 unit.15.2·x2+2·y2+4·x+8·y+2=0Each square = 1 unitStandard form:Type: ____________________Center:Radius:16.8·x2-8·y2+32·x-16·y+56=0Each square = 1 unitStandard form:Type: ____________________Center:Vertices:Foci:math-sheet.comPage 4 / 4

A useful next step

Related activities

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
First page preview: Properties of hyperbolas worksheets

Conic sections

Properties of hyperbolas worksheets

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

Preview and download