Write the equation of the ellipse with center (3, -11), a co-vertex at (15, -11) and b = 13

((x - 3)^2)/(144) + ((y + 11)^2)/(169) = 1

Write the equation of the hyperbola with center (11, -5), a vertex at (23, -5) and b = 13

((x - 11)^2)/(144) - ((y + 5)^2)/(169) = 1

Write the equation of the ellipse with center (-2, 11), a co-vertex at (9, 11) and b = 12

((x + 2)^2)/(121) + ((y - 11)^2)/(144) = 1

Write the equation of the hyperbola with center (-6, -8), a vertex at (6, -8) and b = 11

((x + 6)^2)/(144) - ((y + 8)^2)/(121) = 1

Write the equation of the ellipse with center (-2, 6), a co-vertex at (9, 6) and b = 12

((x + 2)^2)/(121) + ((y - 6)^2)/(144) = 1

Write the equation of the hyperbola with center (2, 7), a vertex at (15, 7) and b = 11

((x - 2)^2)/(169) - ((y - 7)^2)/(121) = 1

Write the equation of the ellipse with center (5, -1), a co-vertex at (16, -1) and b = 13

((x - 5)^2)/(121) + ((y + 1)^2)/(169) = 1

Write the equation of the hyperbola with center (-8, -4), a vertex at (4, -4) and b = 11

((x + 8)^2)/(144) - ((y + 4)^2)/(121) = 1

Write the equation of the ellipse with center (-8, 5), a vertex at (4, 5) and b = 11

((x + 8)^2)/(144) + ((y - 5)^2)/(121) = 1

Write the equation of the hyperbola with center (-5, -10), a vertex at (7, -10) and b = 13

((x + 5)^2)/(144) - ((y + 10)^2)/(169) = 1

Write the equation of the ellipse with center (-6, 11), a vertex at (7, 11) and b = 12

((x + 6)^2)/(169) + ((y - 11)^2)/(144) = 1

Write the equation of the hyperbola with center (-5, 4), a vertex at (8, 4) and b = 11

((x + 5)^2)/(169) - ((y - 4)^2)/(121) = 1

Write the equation of the ellipse with center (9, 0), a co-vertex at (20, 0) and b = 13

((x - 9)^2)/(121) + ((y)^2)/(169) = 1

Write the equation of the hyperbola with center (10, -8), a vertex at (23, -8) and b = 11

((x - 10)^2)/(169) - ((y + 8)^2)/(121) = 1

Write the equation of the ellipse with center (-3, -9), a vertex at (9, -9) and b = 11

((x + 3)^2)/(144) + ((y + 9)^2)/(121) = 1

Write the equation of the hyperbola with center (4, 0), a vertex at (16, 0) and b = 11

((x - 4)^2)/(144) - ((y)^2)/(121) = 1

Write the equation of the ellipse with center (7, 8), a co-vertex at (18, 8) and b = 13

((x - 7)^2)/(121) + ((y - 8)^2)/(169) = 1

Write the equation of the hyperbola with center (-5, -8), a vertex at (6, -8) and b = 13

((x + 5)^2)/(121) - ((y + 8)^2)/(169) = 1

Write the equation of the ellipse with center (3, -9), a co-vertex at (14, -9) and b = 13

((x - 3)^2)/(121) + ((y + 9)^2)/(169) = 1

Write the equation of the hyperbola with center (-6, 11), a vertex at (5, 11) and b = 13

((x + 6)^2)/(121) - ((y - 11)^2)/(169) = 1

Write the equation of the ellipse with center (0, 1), a = 6 and b = 2

((x)^2)/(36) + ((y - 1)^2)/(4) = 1

Write the equation of the hyperbola with center (0, 1), a = 6 and b = 2

((x)^2)/(36) - ((y - 1)^2)/(4) = 1

Worksheets · Precalculus

Precalculus equations of ellipses and hyperbolas worksheet

The two look almost identical on paper: a plus makes an ellipse and a minus makes a hyperbola, and that single sign is the whole difference between a closed curve and two open ones.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Ellipses and Hyperbolas Date Period Write each equation. Write the equation of the ellipse with center $(3, - 11)$ , a co-vertex at $(15, - 11)$ and $b = 13$ Write the equation of the hyperbola with center $(11, - 5)$ , a vertex at $(23, - 5)$ and $b = 13$ Write the equation of the ellipse with center $(- 2, 11)$ , a co-vertex at $(9, 11)$ and $b = 12$ Write the equation of the hyperbola with center $(- 6, - 8)$ , a vertex at $(6, - 8)$ and $b = 11$ Write the equation of the ellipse with center $(- 2, 6)$ , a co-vertex at $(9, 6)$ and $b = 12$ Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(15, 7)$ and $b = 11$ Write the equation of the ellipse with center $(5, - 1)$ , a co-vertex at $(16, - 1)$ and $b = 13$ Write the equation of the hyperbola with center $(- 8, - 4)$ , a vertex at $(4, - 4)$ and $b = 11$ Write the equation of the ellipse with center $(- 8, 5)$ , a vertex at $(4, 5)$ and $b = 11$ Write the equation of the hyperbola with center $(- 5, - 10)$ , a vertex at $(7, - 10)$ and $b = 13$ Write the equation of the ellipse with center $(- 6, 11)$ , a vertex at $(7, 11)$ and $b = 12$ Write the equation of the hyperbola with center $(- 5, 4)$ , a vertex at $(8, 4)$ and $b = 11$ Write the equation of the ellipse with center $(9, 0)$ , a co-vertex at $(20, 0)$ and $b = 13$ Write the equation of the hyperbola with center $(10, - 8)$ , a vertex at $(23, - 8)$ and $b = 11$ Write the equation of the ellipse with center $(- 3, - 9)$ , a vertex at $(9, - 9)$ and $b = 11$ Write the equation of the hyperbola with center $(4, 0)$ , a vertex at $(16, 0)$ and $b = 11$ Write the equation of the ellipse with center $(7, 8)$ , a co-vertex at $(18, 8)$ and $b = 13$ Write the equation of the hyperbola with center $(- 5, - 8)$ , a vertex at $(6, - 8)$ and $b = 13$ Write the equation of the ellipse with center $(3, - 9)$ , a co-vertex at $(14, - 9)$ and $b = 13$ Write the equation of the hyperbola with center $(- 6, 11)$ , a vertex at $(5, 11)$ and $b = 13$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Ellipses and Hyperbolas

Date Period

Write each equation.

Write the equation of the ellipse with center $(3, - 11)$ , a co-vertex at $(15, - 11)$ and $b = 13$
Write the equation of the hyperbola with center $(11, - 5)$ , a vertex at $(23, - 5)$ and $b = 13$
Write the equation of the ellipse with center $(- 2, 11)$ , a co-vertex at $(9, 11)$ and $b = 12$
Write the equation of the hyperbola with center $(- 6, - 8)$ , a vertex at $(6, - 8)$ and $b = 11$
Write the equation of the ellipse with center $(- 2, 6)$ , a co-vertex at $(9, 6)$ and $b = 12$
Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(15, 7)$ and $b = 11$
Write the equation of the ellipse with center $(5, - 1)$ , a co-vertex at $(16, - 1)$ and $b = 13$
Write the equation of the hyperbola with center $(- 8, - 4)$ , a vertex at $(4, - 4)$ and $b = 11$
Write the equation of the ellipse with center $(- 8, 5)$ , a vertex at $(4, 5)$ and $b = 11$
Write the equation of the hyperbola with center $(- 5, - 10)$ , a vertex at $(7, - 10)$ and $b = 13$
Write the equation of the ellipse with center $(- 6, 11)$ , a vertex at $(7, 11)$ and $b = 12$
Write the equation of the hyperbola with center $(- 5, 4)$ , a vertex at $(8, 4)$ and $b = 11$
Write the equation of the ellipse with center $(9, 0)$ , a co-vertex at $(20, 0)$ and $b = 13$
Write the equation of the hyperbola with center $(10, - 8)$ , a vertex at $(23, - 8)$ and $b = 11$
Write the equation of the ellipse with center $(- 3, - 9)$ , a vertex at $(9, - 9)$ and $b = 11$
Write the equation of the hyperbola with center $(4, 0)$ , a vertex at $(16, 0)$ and $b = 11$
Write the equation of the ellipse with center $(7, 8)$ , a co-vertex at $(18, 8)$ and $b = 13$
Write the equation of the hyperbola with center $(- 5, - 8)$ , a vertex at $(6, - 8)$ and $b = 13$
Write the equation of the ellipse with center $(3, - 9)$ , a co-vertex at $(14, - 9)$ and $b = 13$
Write the equation of the hyperbola with center $(- 6, 11)$ , a vertex at $(5, 11)$ and $b = 13$



Sigma Prep · sigmaprep.io/worksheets Name Ellipses and HyperbolasAnswer keyVersion 1 Date Period Write each equation. Write the equation of the ellipse with center $(3, - 11)$ , a co-vertex at $(15, - 11)$ and $b = 13$ $\frac{{(x - 3)}^{2}}{144} + \frac{{(y + 11)}^{2}}{169} = 1$ Write the equation of the hyperbola with center $(11, - 5)$ , a vertex at $(23, - 5)$ and $b = 13$ $\frac{{(x - 11)}^{2}}{144} - \frac{{(y + 5)}^{2}}{169} = 1$ Write the equation of the ellipse with center $(- 2, 11)$ , a co-vertex at $(9, 11)$ and $b = 12$ $\frac{{(x + 2)}^{2}}{121} + \frac{{(y - 11)}^{2}}{144} = 1$ Write the equation of the hyperbola with center $(- 6, - 8)$ , a vertex at $(6, - 8)$ and $b = 11$ $\frac{{(x + 6)}^{2}}{144} - \frac{{(y + 8)}^{2}}{121} = 1$ Write the equation of the ellipse with center $(- 2, 6)$ , a co-vertex at $(9, 6)$ and $b = 12$ $\frac{{(x + 2)}^{2}}{121} + \frac{{(y - 6)}^{2}}{144} = 1$ Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(15, 7)$ and $b = 11$ $\frac{{(x - 2)}^{2}}{169} - \frac{{(y - 7)}^{2}}{121} = 1$ Write the equation of the ellipse with center $(5, - 1)$ , a co-vertex at $(16, - 1)$ and $b = 13$ $\frac{{(x - 5)}^{2}}{121} + \frac{{(y + 1)}^{2}}{169} = 1$ Write the equation of the hyperbola with center $(- 8, - 4)$ , a vertex at $(4, - 4)$ and $b = 11$ $\frac{{(x + 8)}^{2}}{144} - \frac{{(y + 4)}^{2}}{121} = 1$ Write the equation of the ellipse with center $(- 8, 5)$ , a vertex at $(4, 5)$ and $b = 11$ $\frac{{(x + 8)}^{2}}{144} + \frac{{(y - 5)}^{2}}{121} = 1$ Write the equation of the hyperbola with center $(- 5, - 10)$ , a vertex at $(7, - 10)$ and $b = 13$ $\frac{{(x + 5)}^{2}}{144} - \frac{{(y + 10)}^{2}}{169} = 1$ Write the equation of the ellipse with center $(- 6, 11)$ , a vertex at $(7, 11)$ and $b = 12$ $\frac{{(x + 6)}^{2}}{169} + \frac{{(y - 11)}^{2}}{144} = 1$ Write the equation of the hyperbola with center $(- 5, 4)$ , a vertex at $(8, 4)$ and $b = 11$ $\frac{{(x + 5)}^{2}}{169} - \frac{{(y - 4)}^{2}}{121} = 1$ Write the equation of the ellipse with center $(9, 0)$ , a co-vertex at $(20, 0)$ and $b = 13$ $\frac{{(x - 9)}^{2}}{121} + \frac{{(y)}^{2}}{169} = 1$ Write the equation of the hyperbola with center $(10, - 8)$ , a vertex at $(23, - 8)$ and $b = 11$ $\frac{{(x - 10)}^{2}}{169} - \frac{{(y + 8)}^{2}}{121} = 1$ Write the equation of the ellipse with center $(- 3, - 9)$ , a vertex at $(9, - 9)$ and $b = 11$ $\frac{{(x + 3)}^{2}}{144} + \frac{{(y + 9)}^{2}}{121} = 1$ Write the equation of the hyperbola with center $(4, 0)$ , a vertex at $(16, 0)$ and $b = 11$ $\frac{{(x - 4)}^{2}}{144} - \frac{{(y)}^{2}}{121} = 1$ Write the equation of the ellipse with center $(7, 8)$ , a co-vertex at $(18, 8)$ and $b = 13$ $\frac{{(x - 7)}^{2}}{121} + \frac{{(y - 8)}^{2}}{169} = 1$ Write the equation of the hyperbola with center $(- 5, - 8)$ , a vertex at $(6, - 8)$ and $b = 13$ $\frac{{(x + 5)}^{2}}{121} - \frac{{(y + 8)}^{2}}{169} = 1$ Write the equation of the ellipse with center $(3, - 9)$ , a co-vertex at $(14, - 9)$ and $b = 13$ $\frac{{(x - 3)}^{2}}{121} + \frac{{(y + 9)}^{2}}{169} = 1$ Write the equation of the hyperbola with center $(- 6, 11)$ , a vertex at $(5, 11)$ and $b = 13$ $\frac{{(x + 6)}^{2}}{121} - \frac{{(y - 11)}^{2}}{169} = 1$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Ellipses and HyperbolasAnswer keyVersion 1

Date Period

Write each equation.

Write the equation of the ellipse with center $(3, - 11)$ , a co-vertex at $(15, - 11)$ and $b = 13$ $\frac{{(x - 3)}^{2}}{144} + \frac{{(y + 11)}^{2}}{169} = 1$
Write the equation of the hyperbola with center $(11, - 5)$ , a vertex at $(23, - 5)$ and $b = 13$ $\frac{{(x - 11)}^{2}}{144} - \frac{{(y + 5)}^{2}}{169} = 1$
Write the equation of the ellipse with center $(- 2, 11)$ , a co-vertex at $(9, 11)$ and $b = 12$ $\frac{{(x + 2)}^{2}}{121} + \frac{{(y - 11)}^{2}}{144} = 1$
Write the equation of the hyperbola with center $(- 6, - 8)$ , a vertex at $(6, - 8)$ and $b = 11$ $\frac{{(x + 6)}^{2}}{144} - \frac{{(y + 8)}^{2}}{121} = 1$
Write the equation of the ellipse with center $(- 2, 6)$ , a co-vertex at $(9, 6)$ and $b = 12$ $\frac{{(x + 2)}^{2}}{121} + \frac{{(y - 6)}^{2}}{144} = 1$
Write the equation of the hyperbola with center $(2, 7)$ , a vertex at $(15, 7)$ and $b = 11$ $\frac{{(x - 2)}^{2}}{169} - \frac{{(y - 7)}^{2}}{121} = 1$
Write the equation of the ellipse with center $(5, - 1)$ , a co-vertex at $(16, - 1)$ and $b = 13$ $\frac{{(x - 5)}^{2}}{121} + \frac{{(y + 1)}^{2}}{169} = 1$
Write the equation of the hyperbola with center $(- 8, - 4)$ , a vertex at $(4, - 4)$ and $b = 11$ $\frac{{(x + 8)}^{2}}{144} - \frac{{(y + 4)}^{2}}{121} = 1$
Write the equation of the ellipse with center $(- 8, 5)$ , a vertex at $(4, 5)$ and $b = 11$ $\frac{{(x + 8)}^{2}}{144} + \frac{{(y - 5)}^{2}}{121} = 1$
Write the equation of the hyperbola with center $(- 5, - 10)$ , a vertex at $(7, - 10)$ and $b = 13$ $\frac{{(x + 5)}^{2}}{144} - \frac{{(y + 10)}^{2}}{169} = 1$
Write the equation of the ellipse with center $(- 6, 11)$ , a vertex at $(7, 11)$ and $b = 12$ $\frac{{(x + 6)}^{2}}{169} + \frac{{(y - 11)}^{2}}{144} = 1$
Write the equation of the hyperbola with center $(- 5, 4)$ , a vertex at $(8, 4)$ and $b = 11$ $\frac{{(x + 5)}^{2}}{169} - \frac{{(y - 4)}^{2}}{121} = 1$
Write the equation of the ellipse with center $(9, 0)$ , a co-vertex at $(20, 0)$ and $b = 13$ $\frac{{(x - 9)}^{2}}{121} + \frac{{(y)}^{2}}{169} = 1$
Write the equation of the hyperbola with center $(10, - 8)$ , a vertex at $(23, - 8)$ and $b = 11$ $\frac{{(x - 10)}^{2}}{169} - \frac{{(y + 8)}^{2}}{121} = 1$
Write the equation of the ellipse with center $(- 3, - 9)$ , a vertex at $(9, - 9)$ and $b = 11$ $\frac{{(x + 3)}^{2}}{144} + \frac{{(y + 9)}^{2}}{121} = 1$
Write the equation of the hyperbola with center $(4, 0)$ , a vertex at $(16, 0)$ and $b = 11$ $\frac{{(x - 4)}^{2}}{144} - \frac{{(y)}^{2}}{121} = 1$
Write the equation of the ellipse with center $(7, 8)$ , a co-vertex at $(18, 8)$ and $b = 13$ $\frac{{(x - 7)}^{2}}{121} + \frac{{(y - 8)}^{2}}{169} = 1$
Write the equation of the hyperbola with center $(- 5, - 8)$ , a vertex at $(6, - 8)$ and $b = 13$ $\frac{{(x + 5)}^{2}}{121} - \frac{{(y + 8)}^{2}}{169} = 1$
Write the equation of the ellipse with center $(3, - 9)$ , a co-vertex at $(14, - 9)$ and $b = 13$ $\frac{{(x - 3)}^{2}}{121} + \frac{{(y + 9)}^{2}}{169} = 1$
Write the equation of the hyperbola with center $(- 6, 11)$ , a vertex at $(5, 11)$ and $b = 13$ $\frac{{(x + 6)}^{2}}{121} - \frac{{(y - 11)}^{2}}{169} = 1$

How to do these

Write the equation of the ellipse with center $(2, - 1)$ , $a = 5$ and $b = 3$

The center goes in with the opposite sign.
a and b are squared underneath.

The answer is $\frac{{(x - 2)}^{2}}{25} + \frac{{(y + 1)}^{2}}{9} = 1$ .

Where students go wrong

Putting a and b in without squaring them. The denominators are a squared and b squared, so a = 5 gives 25 underneath. The other one is losing track of which letter goes with which axis.

Also called standard form of an ellipse, standard form of a hyperbola or conic equations.

What you can put on this worksheet

Write the equation of an ellipse: Write the equation of the ellipse with center $(0, 1)$ , $a = 6$ and $b = 2$ → $\frac{{(x)}^{2}}{36} + \frac{{(y - 1)}^{2}}{4} = 1$
Write the equation of a hyperbola: Write the equation of the hyperbola with center $(0, 1)$ , $a = 6$ and $b = 2$ → $\frac{{(x)}^{2}}{36} - \frac{{(y - 1)}^{2}}{4} = 1$

Questions about these worksheets

Yes. Every equations of ellipses and 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 ellipses and 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 two 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 2: write the equation of an ellipse and write the equation of a hyperbola. Tick as many as you want and set how many of each, or let it spread them evenly.

Putting a and b in without squaring them. The denominators are a squared and b squared, so a = 5 gives 25 underneath. The other one is losing track of which letter goes with which axis.

Precalculus equations of ellipses and hyperbolas worksheet

Select your difficulty

Ellipses and Hyperbolas

Ellipses and HyperbolasAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these equations of ellipses and hyperbolas worksheets free?+

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

Are these equations of ellipses and hyperbolas worksheets printable?+

What grade are these equations of ellipses and hyperbolas worksheets for?+

Can I get a different version of the same equations of ellipses and hyperbolas worksheet?+

Is this a free alternative to Kuta Software for equations of ellipses and hyperbolas?+

Can I choose how hard the equations of ellipses and hyperbolas questions are?+

What kinds of question are on a equations of ellipses and hyperbolas worksheet?+

What do students get wrong with equations of ellipses and hyperbolas?+