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?
Ren writes an oval flower bed's edge as 25x² + 4y² + 100x + 16y + 16 = 0. Where is its center?
4.
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)²/4 + (y + 2)²/9 = 1
- (x − 1)²/36 + (y + 2)²/16 = 1
- (x − 1)²/16 + (y + 2)²/36 = 1
5.
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)²/16 + (y + 1)²/36 = 1
- (x + 3)²/36 + (y − 1)²/16 = 1
- (x + 3)²/16 + (y − 1)²/36 = 1
- (x + 3)²/9 + (y − 1)²/4 = 1
6.
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)²/16 + (y − 1)²/100 = 1
- (x + 3)²/100 + (y + 1)²/16 = 1
- (x − 3)²/4 + (y − 1)²/25 = 1
- (x − 3)²/100 + (y − 1)²/16 = 1
7.
Luz marks an oval flower bed with stakes at the foci (1, 2) and (7, 2). Every edge point's two distances to the stakes add to 10. Which equation is the edge?
- (x − 4)²/25 + (y − 2)²/16 = 1
- (x − 4)²/25 + (y − 2)²/34 = 1
- (x + 4)²/25 + (y + 2)²/16 = 1
- (x − 4)²/100 + (y − 2)²/91 = 1
8.
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)²/9 + (y − 3)²/25 = 1
- (x + 2)²/84 + (y − 3)²/100 = 1
- (x + 2)²/41 + (y − 3)²/25 = 1
9.
Noah draws a planet's orbit with the sun at one focus; the foci are (-4, 3) and (6, 3). The two distances to the foci always add to 26. Which equation is the orbit?
- (x − 1)²/169 + (y − 3)²/144 = 1
- (x + 1)²/169 + (y + 3)²/144 = 1
- (x − 1)²/676 + (y − 3)²/651 = 1
- (x − 1)²/169 + (y − 3)²/194 = 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)²/34 + (y + 2)²/25 = 1
- (x − 3)²/16 + (y + 2)²/25 = 1
- (x − 3)²/91 + (y + 2)²/100 = 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)
Ren writes an oval flower bed's edge as 25x² + 4y² + 100x + 16y + 16 = 0. Where is its center?
(-2, -2)
4.
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)²/4 + (y + 2)²/9 = 1
- (x − 1)²/36 + (y + 2)²/16 = 1
- (x − 1)²/16 + (y + 2)²/36 = 1
5.
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)²/16 + (y + 1)²/36 = 1
- (x + 3)²/36 + (y − 1)²/16 = 1
- (x + 3)²/16 + (y − 1)²/36 = 1
- (x + 3)²/9 + (y − 1)²/4 = 1
6.
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)²/16 + (y − 1)²/100 = 1
- (x + 3)²/100 + (y + 1)²/16 = 1
- (x − 3)²/4 + (y − 1)²/25 = 1
- (x − 3)²/100 + (y − 1)²/16 = 1
7.
Luz marks an oval flower bed with stakes at the foci (1, 2) and (7, 2). Every edge point's two distances to the stakes add to 10. Which equation is the edge?
- (x − 4)²/25 + (y − 2)²/16 = 1
- (x − 4)²/25 + (y − 2)²/34 = 1
- (x + 4)²/25 + (y + 2)²/16 = 1
- (x − 4)²/100 + (y − 2)²/91 = 1
8.
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)²/9 + (y − 3)²/25 = 1
- (x + 2)²/84 + (y − 3)²/100 = 1
- (x + 2)²/41 + (y − 3)²/25 = 1
9.
Noah draws a planet's orbit with the sun at one focus; the foci are (-4, 3) and (6, 3). The two distances to the foci always add to 26. Which equation is the orbit?
- (x − 1)²/169 + (y − 3)²/144 = 1
- (x + 1)²/169 + (y + 3)²/144 = 1
- (x − 1)²/676 + (y − 3)²/651 = 1
- (x − 1)²/169 + (y − 3)²/194 = 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)²/34 + (y + 2)²/25 = 1
- (x − 3)²/16 + (y + 2)²/25 = 1
- (x − 3)²/91 + (y + 2)²/100 = 1