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<p>In this paper, envelopes of a family of parabolas in the plane are investigated. For a given family of parabolas, we obtain a necessary and sufficient condition concerning if the family of parabolas creates an envelope. Furthermore, we study the relation among an envelope of a family of parabolas in the plane and an envelope of the family of directrixes corresponding to the family of parabolas.</p>

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Envelopes created by families of parabolas in the plane

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • Rion Murakami,
  • Takahiro Yamamoto

摘要

In this paper, envelopes of a family of parabolas in the plane are investigated. For a given family of parabolas, we obtain a necessary and sufficient condition concerning if the family of parabolas creates an envelope. Furthermore, we study the relation among an envelope of a family of parabolas in the plane and an envelope of the family of directrixes corresponding to the family of parabolas.