Parabolas: focus, directrix and equations

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Noah draws a lamp reflector's curve as (x − 2)² = 8(y + 1). The bulb goes at the focus. Where is the focus?

   (2, 1)
2. 2.

   Tala draws a fountain's arc of water as (x + 4)² = -12(y − 2). Where is its focus?

   (-4, -1)
3. 3.

   Zee sketches the parabola (y + 2)² = -16(x + 3) on graph paper. Where is its focus?

   (-7, -2)
4. 4.

   Jun draws the parabola (y + 3)² = 8(x − 2) on graph paper. Which line is its directrix?

   • x = 4
   • x = 0
   • x = -6
   • x = -4
5. 5.

   Luz draws a fountain's arc of water as (x + 2)² = -16(y − 1). Which line is its directrix?

   • y = 5
   • y = -3
   • y = 17
   • y = 3
6. 6.

   Milo sketches the parabola (y − 4)² = -20(x + 1) on graph paper. Which line is its directrix?

   • x = -6
   • x = 4
   • x = 19
   • x = 6
7. 7.

   Noah draws the parabola (y − 3)² = 8(x + 1) on graph paper. Which line is its axis of symmetry?

   • y = -3
   • x = -1
   • y = 3
   • x = 1
8. 8.

   Zee designs a lamp reflector with its focus at (0, 3) and its directrix y = -3. Which equation is the reflector's curve?

   • x² = 3y
   • x² = 24y
   • x² = 12y
   • y² = 12x
9. 9.

   Esme marks the focus (-5, 0) and the directrix x = 5 on graph paper. Which equation is the parabola?

   • y² = -20x
   • y² = -5x
   • y² = -40x
   • x² = -20y
10. 10.

    Jun plans a fountain's arc of water with focus (0, -2) and directrix y = 2. Which equation is the arc?

    • x² = -8y
    • y² = -8x
    • x² = -2y
    • x² = -16y