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Conic sections

Written by Hassan Raza (Mathematics)

8 Class 12 Mathematics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers
  1. The equation x² + y² = 25 represents a circle of radius:

    • 1 50
    • 2 25
    • 3 12.5
    • 4 5
    Show answer

    Correct answer: 5

    r² = 25, so r = 5.

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  2. The focus of the parabola y² = 4x is at:

    • 1 (2, 0)
    • 2 (1, 0)
    • 3 (4, 0)
    • 4 (0, 1)
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    Correct answer: (1, 0)

    For y² = 4ax the focus is (a, 0), with a = 1.

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  3. The eccentricity of a parabola is:

    • 1 Greater than 1
    • 2 0
    • 3 1
    • 4 Less than 1
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    Correct answer: 1

    A parabola has e = 1.

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  4. The centre of the circle (x - 2)² + (y + 3)² = 16 is:

    • 1 (-2, -3)
    • 2 (2, -3)
    • 3 (-2, 3)
    • 4 (2, 3)
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    Correct answer: (2, -3)

    The centre is (h, k) in (x - h)² + (y - k)² = r².

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  5. The eccentricity of an ellipse is:

    • 1 Less than 1
    • 2 Equal to 1
    • 3 Greater than 1
    • 4 Zero always
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    Correct answer: Less than 1

    Ellipses have 0 < e < 1.

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  6. The equation y² = 8x is a:

    • 1 Parabola
    • 2 Circle
    • 3 Hyperbola
    • 4 Ellipse
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    Correct answer: Parabola

    It has the form y² = 4ax.

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  7. The centre of the circle x² + y² = 9 is:

    • 1 (0, 9)
    • 2 (3, 3)
    • 3 (0, 0)
    • 4 (9, 0)
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    Correct answer: (0, 0)

    It is centred at the origin.

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  8. The eccentricity of a hyperbola is:

    • 1 Zero
    • 2 Greater than 1
    • 3 Equal to 1
    • 4 Less than 1
    Show answer

    Correct answer: Greater than 1

    Hyperbolas have e > 1.

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