Grade 11 · Math · Algebra 2

11th grade Ellipses: parts, equations and graphs worksheet

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Ellipses: parts, equations and graphs

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Luz writes an ellipse on graph paper as 9x² + 25y² − 36x + 150y + 36 = 0. Where is its center?
Milo writes an oval table top's edge as 4x² + 9y² + 16x − 54y + 61 = 0. Where is its center?
Noah writes a planet's orbit around the sun as 16x² + 9y² − 64x − 18y − 71 = 0. Where is the orbit's center?
Ren writes an oval flower bed's edge as 25x² + 4y² + 100x + 16y + 16 = 0. Where is its center?
5.
Tala writes an ellipse on graph paper as 4x² + 9y² − 8x + 36y − 104 = 0. Which equation is the same ellipse in standard form?
- (x − 1)²/16 + (y + 2)²/36 = 1
- (x − 1)²/36 + (y + 2)²/16 = 1
- (x + 1)²/36 + (y − 2)²/16 = 1
- (x − 1)²/4 + (y + 2)²/9 = 1
6.
Zee writes an oval table top's edge as 9x² + 4y² + 54x − 8y − 59 = 0. Which equation is the same ellipse in standard form?
- (x + 3)²/36 + (y − 1)²/16 = 1
- (x + 3)²/9 + (y − 1)²/4 = 1
- (x + 3)²/16 + (y − 1)²/36 = 1
- (x − 3)²/16 + (y + 1)²/36 = 1
7.
Esme writes an oval flower bed's edge as 4x² + 25y² − 24x − 50y − 339 = 0. Which equation is the same ellipse in standard form?
- (x + 3)²/100 + (y + 1)²/16 = 1
- (x − 3)²/16 + (y − 1)²/100 = 1
- (x − 3)²/100 + (y − 1)²/16 = 1
- (x − 3)²/4 + (y − 1)²/25 = 1
8.
Jun writes a planet's orbit around the sun as 25x² + 4y² + 50x − 16y − 359 = 0. Which equation is the same ellipse in standard form?
- (x − 1)²/16 + (y + 2)²/100 = 1
- (x + 1)²/16 + (y − 2)²/100 = 1
- (x + 1)²/25 + (y − 2)²/4 = 1
- (x + 1)²/100 + (y − 2)²/16 = 1
9.
Milo draws an oval table top with foci (-2, -1) and (-2, 7). For every edge point, the two distances to the foci add to 10. Which equation is the edge?
- (x − 2)²/9 + (y + 3)²/25 = 1
- (x + 2)²/41 + (y − 3)²/25 = 1
- (x + 2)²/84 + (y − 3)²/100 = 1
- (x + 2)²/9 + (y − 3)²/25 = 1
10.
Ren draws an ellipse on graph paper with foci (3, -5) and (3, 1). For every point on it, the two distances to the foci add to 10. Which equation is it?
- (x + 3)²/16 + (y − 2)²/25 = 1
- (x − 3)²/16 + (y + 2)²/25 = 1
- (x − 3)²/34 + (y + 2)²/25 = 1
- (x − 3)²/91 + (y + 2)²/100 = 1

11th grade Ellipses: parts, equations and graphs worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Ellipses: parts, equations and graphs. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the center, vertices, major axis and foci of an ellipse from its equation, with c² = a² − b².
I can write an ellipse's equation from its vertices and foci, or from its foci and the fixed sum of distances.
I can take out the front numbers and complete both squares to write an ellipse in standard form.

Standard: G-GPE.A.3 (+)

Words to know

ellipse: Every point whose two distances to the foci add to the same number.

foci: The two marked points inside an ellipse (one is a focus).

major axis: The longest line across the ellipse, through both foci; its length is 2a.

vertices: The two ends of the major axis.

center: The midpoint of the foci and of the vertices.

a, b, c: Center to a vertex, center to the near edge, center to a focus.

Common mistakes

Your child gave one of the two distances instead of their sum.

Your child added the steps across and up instead of finding the slanted distance.

Your child subtracted the two distances, which is the rule for a hyperbola.

What to say

Ask: how many distances does an ellipse add together?

Ask: is the slanted path shorter than the two steps together?

Ask: on an ellipse, are the distances added or subtracted?

Questions parents ask

What is the most common mistake with ellipses: parts, equations and graphs?

Your child gave one of the two distances instead of their sum.

How can I help my child with ellipses: parts, equations and graphs?

Ask: how many distances does an ellipse add together?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

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