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)²/36 + (y − 2)²/16 = 1
- (x − 1)²/36 + (y + 2)²/16 = 1
- (x − 1)²/16 + (y + 2)²/36 = 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)²/4 + (y − 1)²/25 = 1
- (x − 3)²/16 + (y − 1)²/100 = 1
- (x + 3)²/100 + (y + 1)²/16 = 1
- (x − 3)²/100 + (y − 1)²/16 = 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)²/100 + (y − 2)²/16 = 1
- (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
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)²/9 + (y − 3)²/25 = 1
- (x + 2)²/84 + (y − 3)²/100 = 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)²/91 + (y + 2)²/100 = 1
- (x − 3)²/34 + (y + 2)²/25 = 1
- (x + 3)²/16 + (y − 2)²/25 = 1
- (x − 3)²/16 + (y + 2)²/25 = 1

Ellipses: parts, equations and graphs

Answer Key - Grade 11 Math Worksheet - Challenge Me

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?
(2, -3)
Milo writes an oval table top's edge as 4x² + 9y² + 16x − 54y + 61 = 0. Where is its center?
(-2, 3)
Noah writes a planet's orbit around the sun as 16x² + 9y² − 64x − 18y − 71 = 0. Where is the orbit's center?
(2, 1)
Ren writes an oval flower bed's edge as 25x² + 4y² + 100x + 16y + 16 = 0. Where is its center?
(-2, -2)
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)²/36 + (y − 2)²/16 = 1
- (x − 1)²/36 + (y + 2)²/16 = 1
- (x − 1)²/16 + (y + 2)²/36 = 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)²/4 + (y − 1)²/25 = 1
- (x − 3)²/16 + (y − 1)²/100 = 1
- (x + 3)²/100 + (y + 1)²/16 = 1
- (x − 3)²/100 + (y − 1)²/16 = 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)²/100 + (y − 2)²/16 = 1
- (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
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)²/9 + (y − 3)²/25 = 1
- (x + 2)²/84 + (y − 3)²/100 = 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)²/91 + (y + 2)²/100 = 1
- (x − 3)²/34 + (y + 2)²/25 = 1
- (x + 3)²/16 + (y − 2)²/25 = 1
- (x − 3)²/16 + (y + 2)²/25 = 1