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.

   Esme draws a lamp reflector's curve as x² = 12y. The bulb goes at the focus. Where is the focus?

   (0, 3)
2. 2.

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

   (5, 0)
3. 3.

   Luz draws a fountain's arc of water as the parabola x² = -8y. Where is its focus?

   (0, -2)
4. 4.

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

   (-4, 0)
5. 5.

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

   • y = -4
   • y = 4
   • x = -4
   • y = -16
6. 6.

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

   • x = -24
   • x = 6
   • y = -6
   • x = -6
7. 7.

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

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

   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
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