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NY Regents Geometry The Parabola — practice questions

Explore 6 free The Parabola 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 Parabola questions and exercises with answers

Showing questions 1–6 of 6.

A parabola holds every point equidistant from a fixed point and which other object?Read the answer and worked solution →Which segment of a parabola passes through the focus and runs parallel to the directrix?Read the answer and worked solution →A parabola with vertex at the origin satisfies y squared equals 36x. What is the equation of its directrix?Read the answer and worked solution →Where does the vertex of a parabola sit in relation to its focus and its directrix?Read the answer and worked solution →For the parabola (y - 2) squared equals 12(x + 5), where are the endpoints of the latus rectum?Read the answer and worked solution →Writing x squared minus 6x minus 8y minus 7 equals 0 in standard form gives which vertex and focus?Read the answer and worked solution →

Worked practice questions

A parabola holds every point equidistant from a fixed point and which other object?

  1. A fixed line, the directrix
  2. A second point, the vertex
  3. A fixed circle, the base
  4. A fixed line, the axis
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Correct answer: A. A fixed line, the directrix

1. The fixed point in the definition is the focus. 2. The fixed line it is paired with is the directrix, and the focus never lies on it. 3. Every point of the curve is the same distance from the focus and from the directrix. 4. The axis of symmetry is a different line, one that runs through the focus itself. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.3 The Parabola_

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Which segment of a parabola passes through the focus and runs parallel to the directrix?

  1. The axis of symmetry
  2. The latus rectum
  3. The transverse axis
  4. The tangent line
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Correct answer: B. The latus rectum

1. The segment runs through the focus with both ends on the curve. 2. Because it is parallel to the directrix, it is named the latus rectum. 3. The axis of symmetry also passes through the focus but is perpendicular to the directrix. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.3 The Parabola_

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A parabola with vertex at the origin satisfies y squared equals 36x. What is the equation of its directrix?

  1. x equals negative 36
  2. y equals negative 9
  3. x equals negative 9
  4. x equals positive 9
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Correct answer: C. x equals negative 9

1. The squared variable is y, so the form is y squared equals 4px and the axis is the x-axis. 2. Matching coefficients gives 4p equal to 36, so p is 9. 3. For this form the directrix is the vertical line x equals negative p. 4. So the directrix is x equals negative 9. 5. Answering x equals negative 36 uses the coefficient without dividing by 4. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.3 The Parabola_

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More Mathematics topics

Law of CosinesThe EllipseConic Sections in General FormConic Sections in Polar CoordinatesLaw of SinesThe HyperbolaVectorsGraphs of Polar Equations