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NY Regents Geometry The Ellipse — practice questions

Explore 7 free The Ellipse 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 Ellipse questions and exercises with answers

Showing questions 1–7 of 7.

For every point on an ellipse, which quantity built from the two foci stays constant?Read the answer and worked solution →In the definition of an ellipse, what name is given to each of the two fixed points?Read the answer and worked solution →In an ellipse, which name belongs to the longer of the two axes of symmetry?Read the answer and worked solution →An ellipse centered at the origin has vertices at (13, 0) and (-13, 0) and foci at (12, 0) and (-12, 0). What is b squared?Read the answer and worked solution →An ellipse has vertices at (3, -1) and (3, 9). Where is its center?Read the answer and worked solution →In the standard form of an ellipse, a squared equals 64. How long is the major axis?Read the answer and worked solution →A whispering chamber is a horizontal ellipse 100 feet long and 60 feet wide, centered at the origin. How far apart are its two foci?Read the answer and worked solution →

Worked practice questions

For every point on an ellipse, which quantity built from the two foci stays constant?

  1. The sum of the two distances
  2. The product of the two distances
  3. The larger of the two distances
  4. The ratio of the two distances
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Correct answer: A. The sum of the two distances

1. Pin a string at two fixed points and trace it taut with a pencil. 2. The string length never changes, so the two distances always add to the same total. 3. That constant total is what defines an ellipse, not a product, a ratio or a maximum. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.1 The Ellipse_

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In the definition of an ellipse, what name is given to each of the two fixed points?

  1. Each one is called a vertex
  2. Each one is called a focus
  3. Each one is called a center
  4. Each one is called an axis
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Correct answer: B. Each one is called a focus

1. The two fixed points hold the string that traces the curve. 2. Each of them is called a focus, and the pair together are the foci. 3. The vertices sit at the ends of the major axis, so they are a different pair of points. 4. The center is the single midpoint of both axes, so it cannot be one of the pair. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.1 The Ellipse_

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In an ellipse, which name belongs to the longer of the two axes of symmetry?

  1. The minor axis
  2. The polar axis
  3. The major axis
  4. The conjugate axis
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Correct answer: C. The major axis

1. Every ellipse has two axes of symmetry that cross at its center. 2. The longer one is named the major axis and the shorter one the minor axis. 3. The foci always sit on the major axis, never on the minor axis. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.1 The Ellipse_

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More Mathematics topics

Law of CosinesConic Sections in General FormThe ParabolaConic Sections in Polar CoordinatesLaw of SinesThe HyperbolaVectorsGraphs of Polar Equations