Parabolas: focus, directrix and equations

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Jun draws the parabola y² = 20x on graph paper. Where is its focus?

   (5, 0)
2. 2.

   Milo sketches the parabola y² = -16x on graph paper. Where is its focus?

   (-4, 0)
3. 3.

   Noah draws a lamp reflector's curve as x² = 16y. Which line is the directrix?

   • x = -4
   • y = -16
   • y = 4
   • y = -4
4. 4.

   Ren draws the parabola y² = 24x on graph paper. Which line is its directrix?

   • x = -24
   • x = -6
   • x = 6
   • y = -6
5. 5.

   Tala draws a fountain's arc of water as the parabola x² = -20y. Which line is its directrix?

   • y = 5
   • y = -5
   • y = 20
   • x = 5
6. 6.

   Zee sketches the parabola y² = -8x on graph paper. Which line is its directrix?

   • x = 8
   • y = 2
   • x = 2
   • x = -2
7. 7.

   Esme marks the focus (0, 2), the directrix y = -2 and the point (8, 8) of a parabola on graph paper. How far is (8, 8) from the focus?

   10
8. 8.

   Jun marks the focus (0, 3), the directrix y = -3 and the point (12, 12) of a parabola on a drawing of a lamp reflector. How far is (12, 12) from the focus?

   15
9. 9.

   Luz marks the focus (0, 1), the directrix y = -1 and the point (-6, 9) of a parabola on graph paper in pencil. How far is (-6, 9) from the focus?

   10
10. 10.

    Milo marks the focus (4, 0), the directrix x = -4 and the point (9, 12) of a parabola on graph paper. How far is (9, 12) from the focus?

    13