Write the equation of the hyperbola with center (5, -4), a vertex at (-3, -4) and b = 10

((x - 5)^2)/(64) - ((y + 4)^2)/(100) = 1

Write the equation of the hyperbola with center (-1, -3), a vertex at (-1, 2) and b = 10

((y + 3)^2)/(25) - ((x + 1)^2)/(100) = 1

Write the equation of the hyperbola with center (8, 3), a vertex at (-2, 3) and b = 5

((x - 8)^2)/(100) - ((y - 3)^2)/(25) = 1

Write the equation of the hyperbola with center (10, -2), a vertex at (3, -2) and b = 12

((x - 10)^2)/(49) - ((y + 2)^2)/(144) = 1

Write the equation of the hyperbola with center (-7, -8), a vertex at (-7, -15) and b = 14

((y + 8)^2)/(49) - ((x + 7)^2)/(196) = 1

Write the equation of the hyperbola with center (2, 7), a vertex at (2, -2) and b = 14

((y - 7)^2)/(81) - ((x - 2)^2)/(196) = 1

Write the equation of the hyperbola with center (-9, 9), a vertex at (-9, 4) and b = 7

((y - 9)^2)/(25) - ((x + 9)^2)/(49) = 1

Write the equation of the hyperbola with center (-3, 2), a vertex at (5, 2) and b = 13

((x + 3)^2)/(64) - ((y - 2)^2)/(169) = 1

Write the equation of the hyperbola with center (-1, -3), a vertex at (14, -3) and b = 5

((x + 1)^2)/(225) - ((y + 3)^2)/(25) = 1

Write the equation of the hyperbola with vertices (-12, 6) and (0, 6) and asymptotes y - 6 = plus or minus 4/3(x + 6)

((x + 6)^2)/(36) - ((y - 6)^2)/(64) = 1

Write the equation of the hyperbola with vertices (6, 2) and (6, 6) and foci (6, -3) and (6, 11)

((y - 4)^2)/(4) - ((x - 6)^2)/(45) = 1

Write the equation of the hyperbola with vertices (-10, 6) and (-2, 6) and foci (-13, 6) and (1, 6)

((x + 6)^2)/(16) - ((y - 6)^2)/(33) = 1

Write the equation of the hyperbola with vertices (-4, 2) and (0, 2) and foci (-5, 2) and (1, 2)

((x + 2)^2)/(4) - ((y - 2)^2)/(5) = 1

Write the equation of the hyperbola with vertices (5, -5) and (5, 3) and foci (5, -8) and (5, 6)

((y + 1)^2)/(16) - ((x - 5)^2)/(33) = 1

Write the equation of the hyperbola with vertices (2, -5) and (8, -5) and foci (1, -5) and (9, -5)

((x - 5)^2)/(9) - ((y + 5)^2)/(7) = 1

Write the equation of the hyperbola with vertices (-2, -2) and (-2, 12) and foci (-2, -6) and (-2, 16)

((y - 5)^2)/(49) - ((x + 2)^2)/(72) = 1

Write the equation of the hyperbola with vertices (0, -6) and (4, -6) and foci (-2, -6) and (6, -6)

((x - 2)^2)/(4) - ((y + 6)^2)/(12) = 1

Write the equation of the hyperbola with vertices (-6, -13) and (-6, 3) and asymptotes y + 5 = plus or minus 4/3(x + 6)

((y + 5)^2)/(64) - ((x + 6)^2)/(36) = 1

Write the equation of the hyperbola with vertices (3, -4) and (3, 8) and asymptotes y - 2 = plus or minus 3/4(x - 3)

((y - 2)^2)/(36) - ((x - 3)^2)/(64) = 1

Worksheets · Precalculus

Equations of hyperbolas worksheet for Precalculus

Precalculus writes hyperbolas from their parts: the center with a vertex and b, the vertices with the foci, or the vertices with the asymptotes, using c² = a² + b². Orientation comes first: the branches open toward the vertices, and the squared term for that direction is the positive one with a² under it.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

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



Sigma Prep · sigmaprep.io/worksheets Name Equations of Hyperbolas Date Period Write each equation. Write a hyperbola from its center Write the equation of the hyperbola with center $(5, - 4)$ , a vertex at $(- 3, - 4)$ and $b = 10$ Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(- 1, 2)$ and $b = 10$ Write the equation of the hyperbola with center $(8, 3)$ , a vertex at $(- 2, 3)$ and $b = 5$ Write the equation of the hyperbola with center $(10, - 2)$ , a vertex at $(3, - 2)$ and $b = 12$ Write the equation of the hyperbola with center $(0, 5)$ , a vertex at $(14, 5)$ and $b = 9$ Write the equation of the hyperbola with center $(- 7, - 8)$ , a vertex at $(- 7, - 15)$ and $b = 14$ Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(2, - 2)$ and $b = 14$ Write the equation of the hyperbola with center $(- 9, 9)$ , a vertex at $(- 9, 4)$ and $b = 7$ Write the equation of the hyperbola with center $(- 3, 2)$ , a vertex at $(5, 2)$ and $b = 13$ Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(14, - 3)$ and $b = 5$ Write a hyperbola from vertices and foci Write the equation of the hyperbola with vertices $(- 12, 6)$ and $(0, 6)$ and asymptotes $y - 6 = \pm \frac{4}{3} (x + 6)$ Write the equation of the hyperbola with vertices $(6, 2)$ and $(6, 6)$ and foci $(6, - 3)$ and $(6, 11)$ Write the equation of the hyperbola with vertices $(- 10, 6)$ and $(- 2, 6)$ and foci $(- 13, 6)$ and $(1, 6)$ Write the equation of the hyperbola with vertices $(- 4, 2)$ and $(0, 2)$ and foci $(- 5, 2)$ and $(1, 2)$ Write the equation of the hyperbola with vertices $(5, - 5)$ and $(5, 3)$ and foci $(5, - 8)$ and $(5, 6)$ Write the equation of the hyperbola with vertices $(2, - 5)$ and $(8, - 5)$ and foci $(1, - 5)$ and $(9, - 5)$ Write the equation of the hyperbola with vertices $(- 2, - 2)$ and $(- 2, 12)$ and foci $(- 2, - 6)$ and $(- 2, 16)$ Write the equation of the hyperbola with vertices $(0, - 6)$ and $(4, - 6)$ and foci $(- 2, - 6)$ and $(6, - 6)$ Write the equation of the hyperbola with vertices $(- 6, - 13)$ and $(- 6, 3)$ and asymptotes $y + 5 = \pm \frac{4}{3} (x + 6)$ Write the equation of the hyperbola with vertices $(3, - 4)$ and $(3, 8)$ and asymptotes $y - 2 = \pm \frac{3}{4} (x - 3)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Equations of Hyperbolas

Date Period

Write each equation.

Write a hyperbola from its center
Write the equation of the hyperbola with center $(5, - 4)$ , a vertex at $(- 3, - 4)$ and $b = 10$
Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(- 1, 2)$ and $b = 10$
Write the equation of the hyperbola with center $(8, 3)$ , a vertex at $(- 2, 3)$ and $b = 5$
Write the equation of the hyperbola with center $(10, - 2)$ , a vertex at $(3, - 2)$ and $b = 12$
Write the equation of the hyperbola with center $(0, 5)$ , a vertex at $(14, 5)$ and $b = 9$
Write the equation of the hyperbola with center $(- 7, - 8)$ , a vertex at $(- 7, - 15)$ and $b = 14$
Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(2, - 2)$ and $b = 14$
Write the equation of the hyperbola with center $(- 9, 9)$ , a vertex at $(- 9, 4)$ and $b = 7$
Write the equation of the hyperbola with center $(- 3, 2)$ , a vertex at $(5, 2)$ and $b = 13$
Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(14, - 3)$ and $b = 5$

Write a hyperbola from vertices and foci
Write the equation of the hyperbola with vertices $(- 12, 6)$ and $(0, 6)$ and asymptotes $y - 6 = \pm \frac{4}{3} (x + 6)$
Write the equation of the hyperbola with vertices $(6, 2)$ and $(6, 6)$ and foci $(6, - 3)$ and $(6, 11)$
Write the equation of the hyperbola with vertices $(- 10, 6)$ and $(- 2, 6)$ and foci $(- 13, 6)$ and $(1, 6)$
Write the equation of the hyperbola with vertices $(- 4, 2)$ and $(0, 2)$ and foci $(- 5, 2)$ and $(1, 2)$
Write the equation of the hyperbola with vertices $(5, - 5)$ and $(5, 3)$ and foci $(5, - 8)$ and $(5, 6)$
Write the equation of the hyperbola with vertices $(2, - 5)$ and $(8, - 5)$ and foci $(1, - 5)$ and $(9, - 5)$
Write the equation of the hyperbola with vertices $(- 2, - 2)$ and $(- 2, 12)$ and foci $(- 2, - 6)$ and $(- 2, 16)$
Write the equation of the hyperbola with vertices $(0, - 6)$ and $(4, - 6)$ and foci $(- 2, - 6)$ and $(6, - 6)$
Write the equation of the hyperbola with vertices $(- 6, - 13)$ and $(- 6, 3)$ and asymptotes $y + 5 = \pm \frac{4}{3} (x + 6)$
Write the equation of the hyperbola with vertices $(3, - 4)$ and $(3, 8)$ and asymptotes $y - 2 = \pm \frac{3}{4} (x - 3)$



Sigma Prep · sigmaprep.io/worksheets Name Equations of HyperbolasAnswer keyVersion 2 Date Period Write each equation. Write a hyperbola from its center Write the equation of the hyperbola with center $(5, - 4)$ , a vertex at $(- 3, - 4)$ and $b = 10$ $\frac{{(x - 5)}^{2}}{64} - \frac{{(y + 4)}^{2}}{100} = 1$ Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(- 1, 2)$ and $b = 10$ $\frac{{(y + 3)}^{2}}{25} - \frac{{(x + 1)}^{2}}{100} = 1$ Write the equation of the hyperbola with center $(8, 3)$ , a vertex at $(- 2, 3)$ and $b = 5$ $\frac{{(x - 8)}^{2}}{100} - \frac{{(y - 3)}^{2}}{25} = 1$ Write the equation of the hyperbola with center $(10, - 2)$ , a vertex at $(3, - 2)$ and $b = 12$ $\frac{{(x - 10)}^{2}}{49} - \frac{{(y + 2)}^{2}}{144} = 1$ Write the equation of the hyperbola with center $(0, 5)$ , a vertex at $(14, 5)$ and $b = 9$ $\frac{x^{2}}{196} - \frac{{(y - 5)}^{2}}{81} = 1$ Write the equation of the hyperbola with center $(- 7, - 8)$ , a vertex at $(- 7, - 15)$ and $b = 14$ $\frac{{(y + 8)}^{2}}{49} - \frac{{(x + 7)}^{2}}{196} = 1$ Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(2, - 2)$ and $b = 14$ $\frac{{(y - 7)}^{2}}{81} - \frac{{(x - 2)}^{2}}{196} = 1$ Write the equation of the hyperbola with center $(- 9, 9)$ , a vertex at $(- 9, 4)$ and $b = 7$ $\frac{{(y - 9)}^{2}}{25} - \frac{{(x + 9)}^{2}}{49} = 1$ Write the equation of the hyperbola with center $(- 3, 2)$ , a vertex at $(5, 2)$ and $b = 13$ $\frac{{(x + 3)}^{2}}{64} - \frac{{(y - 2)}^{2}}{169} = 1$ Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(14, - 3)$ and $b = 5$ $\frac{{(x + 1)}^{2}}{225} - \frac{{(y + 3)}^{2}}{25} = 1$ Write a hyperbola from vertices and foci Write the equation of the hyperbola with vertices $(- 12, 6)$ and $(0, 6)$ and asymptotes $y - 6 = \pm \frac{4}{3} (x + 6)$ $\frac{{(x + 6)}^{2}}{36} - \frac{{(y - 6)}^{2}}{64} = 1$ Write the equation of the hyperbola with vertices $(6, 2)$ and $(6, 6)$ and foci $(6, - 3)$ and $(6, 11)$ $\frac{{(y - 4)}^{2}}{4} - \frac{{(x - 6)}^{2}}{45} = 1$ Write the equation of the hyperbola with vertices $(- 10, 6)$ and $(- 2, 6)$ and foci $(- 13, 6)$ and $(1, 6)$ $\frac{{(x + 6)}^{2}}{16} - \frac{{(y - 6)}^{2}}{33} = 1$ Write the equation of the hyperbola with vertices $(- 4, 2)$ and $(0, 2)$ and foci $(- 5, 2)$ and $(1, 2)$ $\frac{{(x + 2)}^{2}}{4} - \frac{{(y - 2)}^{2}}{5} = 1$ Write the equation of the hyperbola with vertices $(5, - 5)$ and $(5, 3)$ and foci $(5, - 8)$ and $(5, 6)$ $\frac{{(y + 1)}^{2}}{16} - \frac{{(x - 5)}^{2}}{33} = 1$ Write the equation of the hyperbola with vertices $(2, - 5)$ and $(8, - 5)$ and foci $(1, - 5)$ and $(9, - 5)$ $\frac{{(x - 5)}^{2}}{9} - \frac{{(y + 5)}^{2}}{7} = 1$ Write the equation of the hyperbola with vertices $(- 2, - 2)$ and $(- 2, 12)$ and foci $(- 2, - 6)$ and $(- 2, 16)$ $\frac{{(y - 5)}^{2}}{49} - \frac{{(x + 2)}^{2}}{72} = 1$ Write the equation of the hyperbola with vertices $(0, - 6)$ and $(4, - 6)$ and foci $(- 2, - 6)$ and $(6, - 6)$ $\frac{{(x - 2)}^{2}}{4} - \frac{{(y + 6)}^{2}}{12} = 1$ Write the equation of the hyperbola with vertices $(- 6, - 13)$ and $(- 6, 3)$ and asymptotes $y + 5 = \pm \frac{4}{3} (x + 6)$ $\frac{{(y + 5)}^{2}}{64} - \frac{{(x + 6)}^{2}}{36} = 1$ Write the equation of the hyperbola with vertices $(3, - 4)$ and $(3, 8)$ and asymptotes $y - 2 = \pm \frac{3}{4} (x - 3)$ $\frac{{(y - 2)}^{2}}{36} - \frac{{(x - 3)}^{2}}{64} = 1$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Equations of HyperbolasAnswer keyVersion 2

Date Period

Write each equation.

Write a hyperbola from its center
Write the equation of the hyperbola with center $(5, - 4)$ , a vertex at $(- 3, - 4)$ and $b = 10$ $\frac{{(x - 5)}^{2}}{64} - \frac{{(y + 4)}^{2}}{100} = 1$
Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(- 1, 2)$ and $b = 10$ $\frac{{(y + 3)}^{2}}{25} - \frac{{(x + 1)}^{2}}{100} = 1$
Write the equation of the hyperbola with center $(8, 3)$ , a vertex at $(- 2, 3)$ and $b = 5$ $\frac{{(x - 8)}^{2}}{100} - \frac{{(y - 3)}^{2}}{25} = 1$
Write the equation of the hyperbola with center $(10, - 2)$ , a vertex at $(3, - 2)$ and $b = 12$ $\frac{{(x - 10)}^{2}}{49} - \frac{{(y + 2)}^{2}}{144} = 1$
Write the equation of the hyperbola with center $(0, 5)$ , a vertex at $(14, 5)$ and $b = 9$ $\frac{x^{2}}{196} - \frac{{(y - 5)}^{2}}{81} = 1$
Write the equation of the hyperbola with center $(- 7, - 8)$ , a vertex at $(- 7, - 15)$ and $b = 14$ $\frac{{(y + 8)}^{2}}{49} - \frac{{(x + 7)}^{2}}{196} = 1$
Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(2, - 2)$ and $b = 14$ $\frac{{(y - 7)}^{2}}{81} - \frac{{(x - 2)}^{2}}{196} = 1$
Write the equation of the hyperbola with center $(- 9, 9)$ , a vertex at $(- 9, 4)$ and $b = 7$ $\frac{{(y - 9)}^{2}}{25} - \frac{{(x + 9)}^{2}}{49} = 1$
Write the equation of the hyperbola with center $(- 3, 2)$ , a vertex at $(5, 2)$ and $b = 13$ $\frac{{(x + 3)}^{2}}{64} - \frac{{(y - 2)}^{2}}{169} = 1$
Write the equation of the hyperbola with center $(- 1, - 3)$ , a vertex at $(14, - 3)$ and $b = 5$ $\frac{{(x + 1)}^{2}}{225} - \frac{{(y + 3)}^{2}}{25} = 1$

Write a hyperbola from vertices and foci
Write the equation of the hyperbola with vertices $(- 12, 6)$ and $(0, 6)$ and asymptotes $y - 6 = \pm \frac{4}{3} (x + 6)$ $\frac{{(x + 6)}^{2}}{36} - \frac{{(y - 6)}^{2}}{64} = 1$
Write the equation of the hyperbola with vertices $(6, 2)$ and $(6, 6)$ and foci $(6, - 3)$ and $(6, 11)$ $\frac{{(y - 4)}^{2}}{4} - \frac{{(x - 6)}^{2}}{45} = 1$
Write the equation of the hyperbola with vertices $(- 10, 6)$ and $(- 2, 6)$ and foci $(- 13, 6)$ and $(1, 6)$ $\frac{{(x + 6)}^{2}}{16} - \frac{{(y - 6)}^{2}}{33} = 1$
Write the equation of the hyperbola with vertices $(- 4, 2)$ and $(0, 2)$ and foci $(- 5, 2)$ and $(1, 2)$ $\frac{{(x + 2)}^{2}}{4} - \frac{{(y - 2)}^{2}}{5} = 1$
Write the equation of the hyperbola with vertices $(5, - 5)$ and $(5, 3)$ and foci $(5, - 8)$ and $(5, 6)$ $\frac{{(y + 1)}^{2}}{16} - \frac{{(x - 5)}^{2}}{33} = 1$
Write the equation of the hyperbola with vertices $(2, - 5)$ and $(8, - 5)$ and foci $(1, - 5)$ and $(9, - 5)$ $\frac{{(x - 5)}^{2}}{9} - \frac{{(y + 5)}^{2}}{7} = 1$
Write the equation of the hyperbola with vertices $(- 2, - 2)$ and $(- 2, 12)$ and foci $(- 2, - 6)$ and $(- 2, 16)$ $\frac{{(y - 5)}^{2}}{49} - \frac{{(x + 2)}^{2}}{72} = 1$
Write the equation of the hyperbola with vertices $(0, - 6)$ and $(4, - 6)$ and foci $(- 2, - 6)$ and $(6, - 6)$ $\frac{{(x - 2)}^{2}}{4} - \frac{{(y + 6)}^{2}}{12} = 1$
Write the equation of the hyperbola with vertices $(- 6, - 13)$ and $(- 6, 3)$ and asymptotes $y + 5 = \pm \frac{4}{3} (x + 6)$ $\frac{{(y + 5)}^{2}}{64} - \frac{{(x + 6)}^{2}}{36} = 1$
Write the equation of the hyperbola with vertices $(3, - 4)$ and $(3, 8)$ and asymptotes $y - 2 = \pm \frac{3}{4} (x - 3)$ $\frac{{(y - 2)}^{2}}{36} - \frac{{(x - 3)}^{2}}{64} = 1$

How to do these

Write the equation of the hyperbola with center $(1, - 2)$ , a vertex at $(4, - 2)$ and a focus at $(6, - 2)$

The vertex is 3 to the right of the center, so a = 3 and the branches open sideways.
The focus is 5 away, so c = 5 and b² = 25 - 9 = 16.

The answer is $\frac{{(x - 1)}^{2}}{9} - \frac{{(y + 2)}^{2}}{16} = 1$ .

Where students go wrong

Subtracting to find b² as for an ellipse. The foci sit beyond the vertices, so c is the largest and b² = c² - a², here 25 - 9 = 16.

Also called standard form of a hyperbola or hyperbola equation.

What you can put on this worksheet

Write the equation of a hyperbola: Write the equation of the hyperbola with center $(0, 1)$ , $a = 6$ , $b = 2$ and a vertical transverse axis → $\frac{{(y - 1)}^{2}}{36} - \frac{x^{2}}{4} = 1$
A hyperbola from its vertices and foci: Write the equation of the hyperbola with vertices $(- 5, 1)$ and $(5, 1)$ and foci $(- 6, 1)$ and $(6, 1)$ → $\frac{x^{2}}{25} - \frac{{(y - 1)}^{2}}{11} = 1$
From foci, asymptotes, axis lengths or a graph: Write the equation of the hyperbola with vertices $(0, 7)$ and $(0, - 7)$ and foci $(0, \sqrt{53})$ and $(0, - \sqrt{53})$ → $\frac{y^{2}}{49} - \frac{x^{2}}{4} = 1$
From surd vertices and conjugate endpoints: Write the equation of the hyperbola with vertices $(5 \sqrt{2}, 1)$ and $(- 5 \sqrt{2}, 1)$ and conjugate-axis endpoints $(0, 1 + 2 \sqrt{2})$ and $(0, 1 - 2 \sqrt{2})$ → $\frac{x^{2}}{50} - \frac{{(y - 1)}^{2}}{8} = 1$
Vertices and the central rectangle perimeter: A hyperbola has vertices $(- 6, 1)$ and $(6, 1)$ and a central rectangle with perimeter $32$ . Write its equation. → $\frac{x^{2}}{36} - \frac{{(y - 1)}^{2}}{4} = 1$

Questions about these worksheets

Yes. Every equations of 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 equations of 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 5: write the equation of a hyperbola, a hyperbola from its vertices and foci, from foci, asymptotes, axis lengths or a graph, from surd vertices and conjugate endpoints and vertices and the central rectangle perimeter. Tick as many as you want and set how many of each, or let it spread them evenly.

Using a plus. It is the only thing separating this from an ellipse, so it is worth checking before anything else.

Equations of hyperbolas worksheet for Precalculus

Select your difficulty

Write a hyperbola from its center

Write a hyperbola from vertices and foci

Write a hyperbola from its center

Write a hyperbola from vertices and foci

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these equations of hyperbolas worksheets free?+

Do the equations of hyperbolas worksheets come with an answer key?+

Are these equations of hyperbolas worksheets printable?+

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What do students get wrong with equations of hyperbolas?+