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Worksheet

Introduction to Hyperbolas

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Show your work for each problem.

  1. 1.
    Which equation represents a hyperbola?
    1. a)
    2. b)
    3. c)
    4. d)
  2. 2.
    The hyperbola opens in which direction?
    1. a)Up and down
    2. b)Diagonally
    3. c)Left and right
    4. d)It does not open
  3. 3.
    For the hyperbola , what is the value of ?
  4. 4.
    For the hyperbola , what is the value of ?
  5. 5.
    What is the correct formula to find (focal distance) in a hyperbola?
    1. a)
    2. b)
    3. c)
    4. d)
  6. 6.
    For the hyperbola , calculate the value of .
  7. 7.
    Find the vertices of the hyperbola .
  8. 8.
    Find the foci of the hyperbola .
  9. 9.
    What are the asymptotes of the hyperbola ?
    1. a)
    2. b)
    3. c)
    4. d)
  10. 10.
    Find the asymptotes of the hyperbola .
  11. 11.
    Find the center, vertices, foci, and asymptotes of .
  12. 12.
    A hyperbola has vertices at and , and foci at and . What is the value of ?
  13. 13.
    The defining property of a hyperbola is that for any point on the curve:
    1. a)The sum of distances to the foci is constant
    2. b)The difference of distances to the foci is constant
    3. c)The product of distances to the foci is constant
    4. d)The ratio of distances to the foci is constant
  14. 14.
    Write the equation of a hyperbola with vertices at and foci at .
  15. 15.
    GPS systems determine location using the intersection of hyperbolas. Why are hyperbolas used instead of circles?
    1. a)Circles are too difficult to calculate
    2. b)GPS measures the difference in arrival times between satellite signals
    3. c)GPS measures exact distances from satellites
    4. d)Hyperbolas are more accurate than circles
Interactive lesson with step-by-step solutions and more practice (free): mathorio.com/en/learn/pre-calculus/conic-sections/hyperbolas-intro