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5.7.6 Reflective Property of a Hyperbola

Chapter 5: Chapter 5 · MATHEMATICS-VOLUME 1 · EN medium

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The lines from the foci to a point on a hyperbola make equal angles with the tangent line at that point (Fig. . ). The light or sound or radio waves directed from one focus is received at the other focus as in the case ellipse (Fig. . ) used in spotting location of ships sailing in deep sea. Example . Two coast guard stations are located km apart at points A ( , ) and B ( , . A distress signal from a ship at P is received at slightly different times by two stations. It is determined that the ship is km farther from station A than it is from station B . Determine the equation of hyperbola that passes through the location of the ship. Fig. . Elliptical ceiling of a whispering gallery m m

📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 220

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The lines from the foci to a point on a hyperbola make equal angles with the tangent line at that point (Fig. . ). The light or sound or radio waves directed from one focus is received at the other focus as in the case ellipse (Fig.

. ) used in spotting location of ships sailing in deep sea. Example . Two coast guard stations are located km apart at points A ( , ) and B ( , .

A distress signal from a ship at P is received at slightly different times by two stations. It is determined that the ship is km farther from station A than it is from station B . Determine the equation of hyperbola that passes through the location of the ship. Fig.

. Elliptical ceiling of a whispering gallery m m

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