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Conic sections

Written by Hassan Raza (Mathematics)

Class 12 · Mathematics · 8 questions

Name: ____________________   Date: ____________

  1. The equation x² + y² = 25 represents a circle of radius:

    • A 50
    • B 25
    • C 12.5
    • D 5

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

    • A (2, 0)
    • B (1, 0)
    • C (4, 0)
    • D (0, 1)

  3. The eccentricity of a parabola is:

    • A Greater than 1
    • B 0
    • C 1
    • D Less than 1

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

    • A (-2, -3)
    • B (2, -3)
    • C (-2, 3)
    • D (2, 3)

  5. The eccentricity of an ellipse is:

    • A Less than 1
    • B Equal to 1
    • C Greater than 1
    • D Zero always

  6. The equation y² = 8x is a:

    • A Parabola
    • B Circle
    • C Hyperbola
    • D Ellipse

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

    • A (0, 9)
    • B (3, 3)
    • C (0, 0)
    • D (9, 0)

  8. The eccentricity of a hyperbola is:

    • A Zero
    • B Greater than 1
    • C Equal to 1
    • D Less than 1

Answer key

1. D, 2. B, 3. C, 4. B, 5. A, 6. A, 7. C, 8. B

  1. r² = 25, so r = 5.

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

  3. A parabola has e = 1.

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

  5. Ellipses have 0 < e < 1.

  6. It has the form y² = 4ax.

  7. It is centred at the origin.

  8. Hyperbolas have e > 1.