Graph ((y - 6)^2)/(9) - x^2/4 = 1

Center (0, 6), opens up and down

Find the asymptotes and foci of y^2/64 - x^2/36 = 1

Asymptotes y = plus or minus 4/3x;; foci (0, -10), (0, 10)

Graph x^2/9 - y^2/16 = 1

Center (0, 0), opens left and right

Find the asymptotes and foci of x^2/25 - y^2/144 = 1

Asymptotes y = plus or minus 12/5x;; foci (-13, 0), (13, 0)

Graph ((x + 1)^2)/(16) - ((y + 2)^2)/(4) = 1

Center (-1, -2), opens left and right

Find the asymptotes and foci of x^2/49 - y^2/576 = 1

Asymptotes y = plus or minus 24/7x;; foci (-25, 0), (25, 0)

Graph ((y - 5)^2)/(16) - ((x + 2)^2)/(16) = 1

Center (-2, 5), opens up and down

Find the asymptotes and foci of y^2/64 - x^2/225 = 1

Asymptotes y = plus or minus 8/15x;; foci (0, -17), (0, 17)

Graph ((x - 4)^2)/(9) - ((y - 1)^2)/(4) = 1

Center (4, 1), opens left and right

Find the asymptotes and foci of y^2/400 - x^2/441 = 1

Asymptotes y = plus or minus 20/21x;; foci (0, -29), (0, 29)

Graph ((x + 7)^2)/(4) - ((y - 3)^2)/(4) = 1

Center (-7, 3), opens left and right

Find the asymptotes and foci of y^2/16 - x^2/9 = 1

Asymptotes y = plus or minus 4/3x;; foci (0, -5), (0, 5)

Graph ((y + 1)^2)/(9) - x^2/16 = 1

Center (0, -1), opens up and down

Find the asymptotes and foci of y^2/576 - x^2/49 = 1

Asymptotes y = plus or minus 24/7x;; foci (0, -25), (0, 25)

Graph x^2/16 - ((y + 4)^2)/(16) = 1

Center (0, -4), opens left and right

Find the asymptotes and foci of y^2/144 - x^2/25 = 1

Asymptotes y = plus or minus 12/5x;; foci (0, -13), (0, 13)

Graph x^2/4 - ((y - 2)^2)/(4) = 1

Center (0, 2), opens left and right

Find the asymptotes and foci of x^2/225 - y^2/64 = 1

Asymptotes y = plus or minus 8/15x;; foci (-17, 0), (17, 0)

Graph ((x + 1)^2)/(9) - ((y - 6)^2)/(4) = 1

Center (-1, 6), opens left and right

Find the asymptotes and foci of x^2/441 - y^2/400 = 1

Asymptotes y = plus or minus 20/21x;; foci (-29, 0), (29, 0)

Graph ((x - 3)^2)/(9) - ((y + 5)^2)/(9) = 1

Center (3, -5), opens left and right

Find the asymptotes and foci of y^2/225 - x^2/64 = 1

Asymptotes y = plus or minus 15/8x;; foci (0, -17), (0, 17)

Give the asymptotes and the lengths of the transverse and conjugate axes: -16x^2 - 64x - 799 = -49y^2 + 98y

Asymptotes y = 4/7x + 15/7, y = -4/7x - 1/7 transverse 8 conjugate 14

Worksheets · Precalculus

Precalculus graphing hyperbolas worksheet

Precalculus starts hyperbolas from the general form, so completing the square comes first. Then it finds the foci with c² = a² + b² and writes the asymptote equations, not just the branches.

Also taught in Algebra 2, 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.



Sigma Prep · sigmaprep.io/worksheets Name Graphing Hyperbolas Date Period Graph each equation, or find what is asked. Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{36} = 1$ Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ Find the asymptotes and foci of $\frac{x^{2}}{25} - \frac{y^{2}}{144} = 1$ Graph $\frac{{(x + 1)}^{2}}{16} - \frac{{(y + 2)}^{2}}{4} = 1$ Find the asymptotes and foci of $\frac{x^{2}}{49} - \frac{y^{2}}{576} = 1$ Graph $\frac{{(y - 5)}^{2}}{16} - \frac{{(x + 2)}^{2}}{16} = 1$ Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{225} = 1$ Graph $\frac{{(x - 4)}^{2}}{9} - \frac{{(y - 1)}^{2}}{4} = 1$ Find the asymptotes and foci of $\frac{y^{2}}{400} - \frac{x^{2}}{441} = 1$ Graph $\frac{{(x + 7)}^{2}}{4} - \frac{{(y - 3)}^{2}}{4} = 1$ Find the asymptotes and foci of $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$ Graph $\frac{{(y + 1)}^{2}}{9} - \frac{x^{2}}{16} = 1$ Find the asymptotes and foci of $\frac{y^{2}}{576} - \frac{x^{2}}{49} = 1$ Graph $\frac{x^{2}}{16} - \frac{{(y + 4)}^{2}}{16} = 1$ Find the asymptotes and foci of $\frac{y^{2}}{144} - \frac{x^{2}}{25} = 1$ Graph $\frac{x^{2}}{4} - \frac{{(y - 2)}^{2}}{4} = 1$ Find the asymptotes and foci of $\frac{x^{2}}{225} - \frac{y^{2}}{64} = 1$ Graph $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 6)}^{2}}{4} = 1$ Find the asymptotes and foci of $\frac{x^{2}}{441} - \frac{y^{2}}{400} = 1$ 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.

Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$
Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{36} = 1$
Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$
Find the asymptotes and foci of $\frac{x^{2}}{25} - \frac{y^{2}}{144} = 1$
Graph $\frac{{(x + 1)}^{2}}{16} - \frac{{(y + 2)}^{2}}{4} = 1$
Find the asymptotes and foci of $\frac{x^{2}}{49} - \frac{y^{2}}{576} = 1$
Graph $\frac{{(y - 5)}^{2}}{16} - \frac{{(x + 2)}^{2}}{16} = 1$
Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{225} = 1$
Graph $\frac{{(x - 4)}^{2}}{9} - \frac{{(y - 1)}^{2}}{4} = 1$
Find the asymptotes and foci of $\frac{y^{2}}{400} - \frac{x^{2}}{441} = 1$
Graph $\frac{{(x + 7)}^{2}}{4} - \frac{{(y - 3)}^{2}}{4} = 1$
Find the asymptotes and foci of $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$
Graph $\frac{{(y + 1)}^{2}}{9} - \frac{x^{2}}{16} = 1$
Find the asymptotes and foci of $\frac{y^{2}}{576} - \frac{x^{2}}{49} = 1$
Graph $\frac{x^{2}}{16} - \frac{{(y + 4)}^{2}}{16} = 1$
Find the asymptotes and foci of $\frac{y^{2}}{144} - \frac{x^{2}}{25} = 1$
Graph $\frac{x^{2}}{4} - \frac{{(y - 2)}^{2}}{4} = 1$
Find the asymptotes and foci of $\frac{x^{2}}{225} - \frac{y^{2}}{64} = 1$
Graph $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 6)}^{2}}{4} = 1$
Find the asymptotes and foci of $\frac{x^{2}}{441} - \frac{y^{2}}{400} = 1$



Sigma Prep · sigmaprep.io/worksheets Name Graphing HyperbolasAnswer keyVersion 1 Date Period Graph each equation, or find what is asked. Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ Center $(0, 6)$ , opens up and down Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{36} = 1$ Asymptotes $y = \pm \frac{4}{3} x$ ; foci $(0, - 10), (0, 10)$ Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ Center $(0, 0)$ , opens left and right Find the asymptotes and foci of $\frac{x^{2}}{25} - \frac{y^{2}}{144} = 1$ Asymptotes $y = \pm \frac{12}{5} x$ ; foci $(- 13, 0), (13, 0)$ Graph $\frac{{(x + 1)}^{2}}{16} - \frac{{(y + 2)}^{2}}{4} = 1$ Center $(- 1, - 2)$ , opens left and right Find the asymptotes and foci of $\frac{x^{2}}{49} - \frac{y^{2}}{576} = 1$ Asymptotes $y = \pm \frac{24}{7} x$ ; foci $(- 25, 0), (25, 0)$ Graph $\frac{{(y - 5)}^{2}}{16} - \frac{{(x + 2)}^{2}}{16} = 1$ Center $(- 2, 5)$ , opens up and down Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{225} = 1$ Asymptotes $y = \pm \frac{8}{15} x$ ; foci $(0, - 17), (0, 17)$ Graph $\frac{{(x - 4)}^{2}}{9} - \frac{{(y - 1)}^{2}}{4} = 1$ Center $(4, 1)$ , opens left and right Find the asymptotes and foci of $\frac{y^{2}}{400} - \frac{x^{2}}{441} = 1$ Asymptotes $y = \pm \frac{20}{21} x$ ; foci $(0, - 29), (0, 29)$ Graph $\frac{{(x + 7)}^{2}}{4} - \frac{{(y - 3)}^{2}}{4} = 1$ Center $(- 7, 3)$ , opens left and right Find the asymptotes and foci of $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$ Asymptotes $y = \pm \frac{4}{3} x$ ; foci $(0, - 5), (0, 5)$ Graph $\frac{{(y + 1)}^{2}}{9} - \frac{x^{2}}{16} = 1$ Center $(0, - 1)$ , opens up and down Find the asymptotes and foci of $\frac{y^{2}}{576} - \frac{x^{2}}{49} = 1$ Asymptotes $y = \pm \frac{24}{7} x$ ; foci $(0, - 25), (0, 25)$ Graph $\frac{x^{2}}{16} - \frac{{(y + 4)}^{2}}{16} = 1$ Center $(0, - 4)$ , opens left and right Find the asymptotes and foci of $\frac{y^{2}}{144} - \frac{x^{2}}{25} = 1$ Asymptotes $y = \pm \frac{12}{5} x$ ; foci $(0, - 13), (0, 13)$ Graph $\frac{x^{2}}{4} - \frac{{(y - 2)}^{2}}{4} = 1$ Center $(0, 2)$ , opens left and right Find the asymptotes and foci of $\frac{x^{2}}{225} - \frac{y^{2}}{64} = 1$ Asymptotes $y = \pm \frac{8}{15} x$ ; foci $(- 17, 0), (17, 0)$ Graph $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 6)}^{2}}{4} = 1$ Center $(- 1, 6)$ , opens left and right Find the asymptotes and foci of $\frac{x^{2}}{441} - \frac{y^{2}}{400} = 1$ Asymptotes $y = \pm \frac{20}{21} x$ ; foci $(- 29, 0), (29, 0)$ 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.

Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ Center $(0, 6)$ , opens up and down
Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{36} = 1$ Asymptotes $y = \pm \frac{4}{3} x$ ;
foci $(0, - 10), (0, 10)$
Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ Center $(0, 0)$ , opens left and right
Find the asymptotes and foci of $\frac{x^{2}}{25} - \frac{y^{2}}{144} = 1$ Asymptotes $y = \pm \frac{12}{5} x$ ;
foci $(- 13, 0), (13, 0)$
Graph $\frac{{(x + 1)}^{2}}{16} - \frac{{(y + 2)}^{2}}{4} = 1$ Center $(- 1, - 2)$ , opens left and right
Find the asymptotes and foci of $\frac{x^{2}}{49} - \frac{y^{2}}{576} = 1$ Asymptotes $y = \pm \frac{24}{7} x$ ;
foci $(- 25, 0), (25, 0)$
Graph $\frac{{(y - 5)}^{2}}{16} - \frac{{(x + 2)}^{2}}{16} = 1$ Center $(- 2, 5)$ , opens up and down
Find the asymptotes and foci of $\frac{y^{2}}{64} - \frac{x^{2}}{225} = 1$ Asymptotes $y = \pm \frac{8}{15} x$ ;
foci $(0, - 17), (0, 17)$
Graph $\frac{{(x - 4)}^{2}}{9} - \frac{{(y - 1)}^{2}}{4} = 1$ Center $(4, 1)$ , opens left and right
Find the asymptotes and foci of $\frac{y^{2}}{400} - \frac{x^{2}}{441} = 1$ Asymptotes $y = \pm \frac{20}{21} x$ ;
foci $(0, - 29), (0, 29)$
Graph $\frac{{(x + 7)}^{2}}{4} - \frac{{(y - 3)}^{2}}{4} = 1$ Center $(- 7, 3)$ , opens left and right
Find the asymptotes and foci of $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$ Asymptotes $y = \pm \frac{4}{3} x$ ;
foci $(0, - 5), (0, 5)$
Graph $\frac{{(y + 1)}^{2}}{9} - \frac{x^{2}}{16} = 1$ Center $(0, - 1)$ , opens up and down
Find the asymptotes and foci of $\frac{y^{2}}{576} - \frac{x^{2}}{49} = 1$ Asymptotes $y = \pm \frac{24}{7} x$ ;
foci $(0, - 25), (0, 25)$
Graph $\frac{x^{2}}{16} - \frac{{(y + 4)}^{2}}{16} = 1$ Center $(0, - 4)$ , opens left and right
Find the asymptotes and foci of $\frac{y^{2}}{144} - \frac{x^{2}}{25} = 1$ Asymptotes $y = \pm \frac{12}{5} x$ ;
foci $(0, - 13), (0, 13)$
Graph $\frac{x^{2}}{4} - \frac{{(y - 2)}^{2}}{4} = 1$ Center $(0, 2)$ , opens left and right
Find the asymptotes and foci of $\frac{x^{2}}{225} - \frac{y^{2}}{64} = 1$ Asymptotes $y = \pm \frac{8}{15} x$ ;
foci $(- 17, 0), (17, 0)$
Graph $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 6)}^{2}}{4} = 1$ Center $(- 1, 6)$ , opens left and right
Find the asymptotes and foci of $\frac{x^{2}}{441} - \frac{y^{2}}{400} = 1$ Asymptotes $y = \pm \frac{20}{21} x$ ;
foci $(- 29, 0), (29, 0)$

How to do these

Find the center and foci of $9 x^{2} - 4 y^{2} - 18 x - 16 y - 43 = 0$

Complete the square: 9(x - 1)² - 4(y + 2)² = 36.
Divide by 36: (x - 1)²/4 - (y + 2)²/9 = 1, so a = 2 and b = 3.
c² = 4 + 9 = 13, and the x term is first, so the foci sit left and right of the center.

The answer is Center $(1, - 2)$ , foci $(1 \pm \sqrt{13}, - 2)$ .

Where students go wrong

Using c² = a² - b², the ellipse rule. For a hyperbola c² = a² + b², so the foci always lie farther from the center than the vertices.

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

What you can put on this worksheet

A hyperbola: Graph $\frac{{(x - 3)}^{2}}{9} - \frac{{(y + 5)}^{2}}{9} = 1$ → Center $(3, - 5)$ , opens left and right
Asymptotes and foci: Find the asymptotes and foci of $\frac{y^{2}}{225} - \frac{x^{2}}{64} = 1$ → Asymptotes $y = \pm \frac{15}{8} x$ ;
foci $(0, - 17), (0, 17)$
Foci with roots, from a scrambled equation: Give the asymptotes and the lengths of the transverse and conjugate axes:
$- 16 x^{2} - 64 x - 799 = - 49 y^{2} + 98 y$ → Asymptotes $y =$ $\frac{4}{7} x +$ $\frac{15}{7},$ $y =$ $- \frac{4}{7} x -$ $\frac{1}{7}$ transverse $8$ conjugate $14$

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.

Precalculus is usually taken around 11th or 12th 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 with roots, from a scrambled equation. 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.

Precalculus graphing hyperbolas worksheet

Graphing Hyperbolas

Graphing HyperbolasAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these graphing hyperbolas worksheets free?+

Do the graphing hyperbolas worksheets come with an answer key?+

Are these graphing hyperbolas worksheets printable?+

What grade are these graphing hyperbolas worksheets for?+

Can I get a different version of the same graphing hyperbolas worksheet?+

Is this a free alternative to Kuta Software for graphing hyperbolas?+

Can I choose how hard the graphing hyperbolas questions are?+

What kinds of question are on a graphing hyperbolas worksheet?+

What do students get wrong with graphing hyperbolas?+