Worksheets · Algebra 2

Graphing hyperbolas worksheet for Algebra 2

Which fraction comes first decides which way a hyperbola opens, and the two numbers underneath give the slopes of the lines it runs alongside. Draw those lines first and the branches have somewhere to go.

Also taught in Precalculus, at its own level and with its own examples.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Hyperbolas

Date Period

Graph each equation, or find what is asked.

  1. Graph a hyperbola

    Graph x29−(y−6)24=1−10−10−5−5551010
  2. Graph 9x2−16y2−90x+81=0−10−10−5−5551010
  3. Graph (x+3)29−(y+1)216=1−10−10−5−5551010
  4. Graph (x−4)29−(y+6)29=1−10−10−5−5551010
  5. Graph −25x2+16y2+128y−144=0−10−10−5−5551010
  6. Graph (x+3)29−(y−6)24=1−10−10−5−5551010
  7. Graph (x+4)29−y24=1−10−10−5−5551010
  8. Graph 16x2−25y2+32x+200y−784=0−10−10−5−5551010
  9. Graph y24−(x+1)216=1−10−10−5−5551010
  10. Graph (x−1)24−(y−3)29=1−10−10−5−5551010

  1. Find the asymptotes and foci

    Find the asymptotes and foci of y2400−x2441=1
  2. Find the asymptotes and foci of x29−y216=1
  3. Find the asymptotes and foci of (y+2)264−(x+1)2225=1
  4. Find the asymptotes and foci of x2144−y225=1
  5. Find the asymptotes and foci of x249−y2576=1
  6. Find the asymptotes and foci of (y−2)2144−(x+1)225=1
  7. Find the asymptotes and foci of x2225−y264=1
  8. Find the asymptotes and foci of x236−y264=1
  9. Find the asymptotes and foci of x2400−(y−1)2441=1
  10. Find the asymptotes and foci of y216−x29=1

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing HyperbolasAnswer keyVersion 1

Date Period

Graph each equation, or find what is asked.

  1. Graph a hyperbola

    Graph x29−(y−6)24=1−10−5−5510−10510Center (0,6), opens left and right
  2. Graph 9x2−16y2−90x+81=0−10−10−551010−5Center (5,0), opens left and right
  3. Graph (x+3)29−(y+1)216=1−10−10−5−5551010Center (−3,−1), opens left and right
  4. Graph (x−4)29−(y+6)29=1−10−5−55510−1010Center (4,−6), opens left and right
  5. Graph −25x2+16y2+128y−144=0−10−5551010−10−5Center (0,−4), opens up and down
  6. Graph (x+3)29−(y−6)24=1−10−10−5−5510105Center (−3,6), opens left and right
  7. Graph (x+4)29−y24=1−10−10−5551010−5Center (−4,0), opens left and right
  8. Graph 16x2−25y2+32x+200y−784=0−10−5−551010−105Center (−1,4), opens left and right
  9. Graph y24−(x+1)216=1−10−10−5−5551010Center (−1,0), opens up and down
  10. Graph (x−1)24−(y−3)29=1−10−10−5−5510105Center (1,3), opens left and right

  1. Find the asymptotes and foci

    Find the asymptotes and foci of y2400−x2441=1Asymptotes y=±2021x;
    foci (0,−29),(0,29)
  2. Find the asymptotes and foci of x29−y216=1Asymptotes y=±43x;
    foci (−5,0),(5,0)
  3. Find the asymptotes and foci of (y+2)264−(x+1)2225=1Asymptotes y+2=±815(x+1);
    foci (−1,−19),(−1,15)
  4. Find the asymptotes and foci of x2144−y225=1Asymptotes y=±512x;
    foci (−13,0),(13,0)
  5. Find the asymptotes and foci of x249−y2576=1Asymptotes y=±247x;
    foci (−25,0),(25,0)
  6. Find the asymptotes and foci of (y−2)2144−(x+1)225=1Asymptotes y−2=±125(x+1);
    foci (−1,−11),(−1,15)
  7. Find the asymptotes and foci of x2225−y264=1Asymptotes y=±815x;
    foci (−17,0),(17,0)
  8. Find the asymptotes and foci of x236−y264=1Asymptotes y=±43x;
    foci (−10,0),(10,0)
  9. Find the asymptotes and foci of x2400−(y−1)2441=1Asymptotes y−1=±2120x;
    foci (−29,1),(29,1)
  10. Find the asymptotes and foci of y216−x29=1Asymptotes y=±43x;
    foci (0,−5),(0,5)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Graph (x+1)29−(y−2)24=1

  1. The x term is first, so it opens left and right.
  2. The center is at (-1, 2), with vertices 3 either side.
  3. The asymptotes run out from the center with slopes of plus and minus two thirds.

The answer is Center (−1,2), opens left and right.

Where students go wrong

Opening it the wrong way. It opens toward whichever variable is positive, not toward the larger number. The other slip is drawing the branches without the asymptotes, which is what makes the shape come out right.

Also called plotting hyperbolas, hyperbola graphs or asymptotes of a hyperbola.

What you can put on this worksheet

A hyperbola
Graph (x−3)29−(y+5)29=1 → Center (3,−5), opens left and right
Asymptotes and foci
Find the asymptotes and foci of y2225−x264=1 → Asymptotes y=±158x;
foci (0,−17),(0,17)
Foci, asymptotes and axes of a hyperbola
Give the asymptotes and the lengths of the transverse and conjugate axes:
−16x2−64x−799=−49y2+98y → Asymptotes y=47x+157, y=−47x−17transverse 8conjugate 14

Questions about these worksheets

Yes. Every graphing hyperbolas sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the graphing hyperbolas questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: a hyperbola, asymptotes and foci and foci, asymptotes and axes of a hyperbola. Tick as many as you want and set how many of each, or let it spread them evenly.

Opening it the wrong way. It opens toward whichever variable is positive, not toward the larger number. The other slip is drawing the branches without the asymptotes, which is what makes the shape come out right.