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 ellipse with center (11, -5), a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center (-5, -10), a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center (-5, -8), a co-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 ellipse with center (-6, 11), a co-vertex at (5, 11) and b = 13

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

Worksheets · Precalculus

Precalculus equations of ellipses worksheet

Two squared parentheses over two squared numbers, added, equal to one. The center goes in with the opposite sign, as it does for a circle.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Equations of Ellipses 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 ellipse with center $(11, - 5)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 10)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 8)$ , a co-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 ellipse with center $(- 6, 11)$ , a co-vertex at $(5, 11)$ and $b = 13$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Equations of Ellipses

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 ellipse with center $(11, - 5)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 10)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 8)$ , a co-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 ellipse with center $(- 6, 11)$ , a co-vertex at $(5, 11)$ and $b = 13$



Sigma Prep · sigmaprep.io/worksheets Name Equations of EllipsesAnswer 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 ellipse with center $(11, - 5)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 10)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 8)$ , a co-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 ellipse with center $(- 6, 11)$ , a co-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

Equations of EllipsesAnswer 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 ellipse with center $(11, - 5)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 10)$ , a co-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 ellipse 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 ellipse 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 ellipse 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 ellipse with center $(- 5, - 8)$ , a co-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 ellipse with center $(- 6, 11)$ , a co-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 underneath without squaring them. a = 5 gives 25, not 5.

Also called standard form of an ellipse or ellipse equation.

Questions about these worksheets

Yes. Every equations of ellipses 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 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.

Putting a and b underneath without squaring them. a = 5 gives 25, not 5.

Precalculus equations of ellipses worksheet

Select your difficulty

Equations of Ellipses

Equations of EllipsesAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these equations of ellipses worksheets free?+

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

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

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