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NY Regents Geometry The Hyperbola — practice questions

Explore 4 free The Hyperbola questions in NY Regents Geometry Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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The Hyperbola questions and exercises with answers

Showing questions 1–4 of 4.

For every point on a hyperbola, which quantity built from the two foci stays constant?Read the answer and worked solution →Which axis of a hyperbola has the two vertices as its endpoints?Read the answer and worked solution →How can the asymptotes of a hyperbola be sketched from its central rectangle?Read the answer and worked solution →A hyperbola has vertices at (2, -3) and (10, -3) and foci at (0, -3) and (12, -3). What is b squared?Read the answer and worked solution →

Worked practice questions

For every point on a hyperbola, which quantity built from the two foci stays constant?

  1. The sum of the distances
  2. The product of the distances
  3. The average of the distances
  4. The difference of the distances
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Correct answer: D. The difference of the distances

1. A hyperbola has two foci, exactly like an ellipse does. 2. What is held fixed here is the difference of the two distances, not their sum. 3. That single change of sum to difference is what splits the curve into two branches. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_

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Which axis of a hyperbola has the two vertices as its endpoints?

  1. The transverse axis
  2. The conjugate axis
  3. The horizontal axis
  4. The asymptote axis
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Correct answer: A. The transverse axis

1. A hyperbola has two axes of symmetry crossing at its center. 2. The one carrying the vertices at its ends is the transverse axis. 3. The conjugate axis is perpendicular to it and carries the co-vertices instead. 4. Calling it the horizontal axis fails because the transverse axis can be vertical. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_

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How can the asymptotes of a hyperbola be sketched from its central rectangle?

  1. Extend the long sides of the rectangle
  2. Extend the short sides of the rectangle
  3. Extend the diagonals of the rectangle
  4. Extend a median of the rectangle
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Correct answer: C. Extend the diagonals of the rectangle

1. Build the central rectangle so its sides pass through each vertex and co-vertex. 2. Draw both diagonals of that rectangle and extend them past the corners. 3. Those extended diagonals are the asymptotes the branches approach. 4. Extending the sides instead gives lines the curve never approaches at all. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_

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More Mathematics topics

Law of CosinesThe EllipseConic Sections in General FormThe ParabolaConic Sections in Polar CoordinatesLaw of SinesVectorsGraphs of Polar Equations