Conic Sections Quiz

Grade 11 · Math · Quiz

Test your ability to identify, write equations for, and analyze all four types of conic sections.

Questions

  1. What is the center and radius of (x+3)² + (y-5)² = 49?

    1. Center (-3, 5), r=7
    2. Center (3, -5), r=7
    3. Center (-3, 5), r=49
    4. Center (3, 5), r=7
    Show answer

    Answer: Center (-3, 5), r=7

    In (x+3)² + (y-5)² = 49, center is (-3, 5) and r = √49 = 7.

  2. Which equation represents an ellipse?

    1. 4x² - y² = 16
    2. x² + y² = 25
    3. 4x² + 9y² = 36
    4. x² = 4y
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    Answer: 4x² + 9y² = 36

    4x² + 9y² = 36 → x²/9 + y²/4 = 1, an ellipse with two different denominators.

  3. The foci of the ellipse x²/36 + y²/20 = 1 are at:

    1. (±4, 0)
    2. (±6, 0)
    3. (0, ±4)
    4. (±√56, 0)
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    Answer: (±4, 0)

    a² = 36, b² = 20; c² = 36 - 20 = 16; c = 4. Foci at (±4, 0) on the major (x) axis.

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

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

    For y²/a² - x²/b² = 1 with a=2 and b=3, asymptotes are y = ±(a/b)x = ±(2/3)x.

  5. A parabola has vertex (0, 0) and directrix y = 5. What is its equation?

    1. x² = 20y
    2. x² = -20y
    3. y² = 20x
    4. x² = 5y
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    Answer: x² = -20y

    Directrix y = 5 means p = -5 (focus below vertex). Equation: x² = 4(-5)y = -20y.

  6. The equation 9x² + 4y² - 18x + 16y - 11 = 0 represents which conic?

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

    Answer: Ellipse

    Group and complete the square: 9(x-1)² + 4(y+2)² = 36 → ellipse (x-1)²/4 + (y+2)²/9 = 1.

  7. The hyperbola and ellipse both have two foci.

    Show answer

    Answer: True

    Both ellipses and hyperbolas are defined using two foci. A parabola has one focus.

  8. For the hyperbola x²/16 - y²/9 = 1, the value of c is ___.

    Show answer

    Answer: 5

    c² = a² + b² = 16 + 9 = 25; c = 5.

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