Ellipses: parts, equations and graphs

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Luz plans an oval flower bed with stakes at the foci (-3, 0) and (3, 0). The edge passes through (3, 8). What is the sum of the point's distances to the foci?

   18
2. 2.

   An ellipse with its foci (0, -6) and (0, 6) marked, and the point (16, 6) on it. Milo draws an oval table top with foci (0, -6) and (0, 6). The edge passes through (16, 6). What is the sum of the point's distances to the foci?

   36
3. 3.

   Noah draws a planet's orbit with foci (-2, 0) and (2, 0), the sun at (2, 0). It passes through (2, 3). What is the sum of the point's distances to the foci?

   8
4. 4.

   Ren draws an ellipse on graph paper with foci (0, -8) and (0, 8). It passes through (12, 8). What is the sum of the point's distances to the foci?

   32
5. 5.

   Zee draws the ellipse x²/25 + y²/81 = 1 on graph paper. How long is its major axis, the longest line across it?

   18
6. 6.

   Esme draws an oval table top as x²/100 + y²/36 = 1, in decimeters. How long is its major axis, the longest line across it?

   20
7. 7.

   Jun draws the ellipse x²/9 + y²/64 = 1 on graph paper. How long is its major axis, the longest line across it?

   16
8. 8.

   Luz draws a planet's orbit around the sun as x²/25 + y²/16 = 1. The sun sits at one focus. Where are the foci?

   • (-√41, 0) and (√41, 0)
   • (-3, 0) and (3, 0)
   • (0, -3) and (0, 3)
   • (-5, 0) and (5, 0)
9. 9.

   Milo plans an oval flower bed as x²/9 + y²/25 = 1, with a stake at each focus. Where are the foci?

   • (0, -√34) and (0, √34)
   • (0, -5) and (0, 5)
   • (0, -4) and (0, 4)
   • (-4, 0) and (4, 0)
10. 10.

    Noah draws the ellipse x²/169 + y²/144 = 1 on graph paper. Where are its foci?

    • (0, -5) and (0, 5)
    • (-13, 0) and (13, 0)
    • (-√313, 0) and (√313, 0)
    • (-5, 0) and (5, 0)