Ellipses: parts, equations and graphs

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Tala draws a planet's orbit around the sun as (x − 2)²/25 + (y + 1)²/9 = 1. Where are the foci?

   • (-6, 1) and (2, 1)
   • (2 − √34, -1) and (2 + √34, -1)
   • (-2, -1) and (6, -1)
   • (2, -5) and (2, 3)
2. 2.

   Zee plans an oval flower bed as (x + 3)²/16 + (y − 2)²/25 = 1, with a stake at each focus. Where are the foci?

   • (3, -5) and (3, 1)
   • (-6, 2) and (0, 2)
   • (-3, -1) and (-3, 5)
   • (-3, 2 − √41) and (-3, 2 + √41)
3. 3.

   Esme draws the ellipse (x − 1)²/100 + (y − 4)²/36 = 1 on graph paper. Where are its foci?

   • (-9, -4) and (7, -4)
   • (1, -4) and (1, 12)
   • (-7, 4) and (9, 4)
   • (1 − 2√34, 4) and (1 + 2√34, 4)
4. 4.

   Jun draws an oval table top as (x + 4)²/64 + (y + 5)²/100 = 1. Where are its foci?

   • (-4, -11) and (-4, 1)
   • (-10, -5) and (2, -5)
   • (-4, -5 − 2√41) and (-4, -5 + 2√41)
   • (4, -1) and (4, 11)
5. 5.

   Luz plans an oval flower bed with vertices (-10, 0) and (10, 0) and foci (-6, 0) and (6, 0). Which equation is it?

   • x²/100 + y²/136 = 1
   • x²/10 + y²/8 = 1
   • x²/64 + y²/100 = 1
   • x²/100 + y²/64 = 1
6. 6.

   Ren draws a planet's orbit around the sun with vertices (0, -5) and (0, 5) and foci (0, -3) and (0, 3). Which equation is it?

   • x²/4 + y²/5 = 1
   • x²/16 + y²/25 = 1
   • x²/34 + y²/25 = 1
   • x²/25 + y²/16 = 1
7. 7.

   Tala draws the ellipse (x − 1)²/36 + (y + 2)²/16 = 1 on graph paper. Where is its highest point?

   (1, 2)
8. 8.

   Zee draws an oval table top as (x + 2)²/9 + (y − 1)²/49 = 1. Where is the point of the edge farthest to the right?

   (1, 1)
9. 9.

   Esme plans an oval flower bed as (x − 3)²/64 + (y − 5)²/25 = 1. Where is the point of the edge farthest to the right?

   (11, 5)
10. 10.

    Jun draws the ellipse (x + 4)²/16 + (y + 3)²/81 = 1 on graph paper. Where is its highest point?

    (-4, 6)