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.

   Tala plans an oval flower bed as x²/49 + y²/16 = 1, in feet. How long is its major axis, the longest line across it?

   14
6. 6.

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

   18
7. 7.

   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
8. 8.

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

   16
9. 9.

   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?

   • (-3, 0) and (3, 0)
   • (-√41, 0) and (√41, 0)
   • (-5, 0) and (5, 0)
   • (0, -3) and (0, 3)
10. 10.

    Ren draws an oval table top as x²/36 + y²/100 = 1. Where are its foci?

    • (0, -8) and (0, 8)
    • (0, -10) and (0, 10)
    • (-8, 0) and (8, 0)
    • (0, -2√34) and (0, 2√34)