Conic Sections Quiz

Grade 11 · Math · Quiz

10 questions on identifying, graphing, and applying equations for all four conic sections.

Questions

1. Which conic does x² + y² = 49 represent?

   1. Ellipse
   2. Circle
   3. Parabola
   4. Hyperbola
   Show answer

   Answer: Circle

   Both variables squared with equal positive coefficients and sum = constant → circle.

2. What is the radius of the circle x² + y² − 6x + 2y + 6 = 0?

   1. 1
   2. 2
   3. 3
   4. 4
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   Answer: 2

   Complete the square: (x−3)² + (y+1)² = 9+1−6 = 4. r = √4 = 2.

3. The parabola y = −(x+2)² + 5 opens in which direction?

   1. Up
   2. Down
   3. Left
   4. Right
   Show answer

   Answer: Down

   The coefficient of (x+2)² is −1 (negative), so the parabola opens downward.

4. For the ellipse x²/49 + y²/36 = 1, which axis is the major axis?

   1. x-axis (horizontal)
   2. y-axis (vertical)
   3. Both equal
   4. Neither
   Show answer

   Answer: x-axis (horizontal)

   a² = 49 > b² = 36, so the major axis is along the x-axis.

5. Find c for the ellipse x²/25 + y²/16 = 1.

   1. c = 2
   2. c = 3
   3. c = 4
   4. c = 5
   Show answer

   Answer: c = 3

   c² = a² − b² = 25 − 16 = 9, so c = 3.

6. What are the asymptotes of the hyperbola x²/4 − y²/9 = 1?

   1. y = ±(2/3)x
   2. y = ±(3/2)x
   3. y = ±2x
   4. y = ±9x
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   Answer: y = ±(3/2)x

   Asymptotes: y = ±(b/a)x = ±(3/2)x.

7. The vertex of y = (x − 4)² − 7 is at:

   1. (4, 7)
   2. (4, −7)
   3. (−4, 7)
   4. (−4, −7)
   Show answer

   Answer: (4, −7)

   Vertex form y = (x−h)² + k: vertex = (4, −7).

8. Which equation represents an ellipse (not a circle)?

   1. x² + y² = 16
   2. x²/9 + y²/4 = 1
   3. x²/9 − y²/4 = 1
   4. y = x² + 1
   Show answer

   Answer: x²/9 + y²/4 = 1

   Both terms positive, sum = 1, but a² ≠ b² → ellipse, not circle.

9. A hyperbola has equation y²/16 − x²/9 = 1. Its branches open in which direction?

   1. Left and right
   2. Up and down
   3. Diagonally
   4. They do not open
   Show answer

   Answer: Up and down

   The positive term is y², so branches open up and down.

10. What is the eccentricity of a parabola?

    1. 0
    2. Between 0 and 1
    3. 1
    4. Greater than 1
    Show answer

    Answer: 1

    By definition, all parabolas have eccentricity e = 1.

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