5.7.3 Hyperbola
Chapter 5: Chapter 5 · MATHEMATICS-VOLUME 1 · EN medium
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Some Comets travel in hyperbolic paths with the Sun at one focus, such comets pass by the Sun only one time unlike those in elliptical orbits, which reappear at intervals. We also see hyperbolas in architecture, such as Mumbai Airport terminal (Fig. . ), in cross section of a planetarium, an locating ships (Fig. . ), or a cooling tower for a steam or nuclear power plant. (Fig. . Example . A semielliptical archway over a one-way road has a height of m and a width of m . The truck has a width of m and a height of . m . Will the truck clear the opening of the archway? (Fig. . ) Since the truck’s width is3 m , to determine the clearance, we must find the height of the archway .
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 216
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Some Comets travel in hyperbolic paths with the Sun at one focus, such comets pass by the Sun only one time unlike those in elliptical orbits, which reappear at intervals. We also see hyperbolas in architecture, such as Mumbai Airport terminal (Fig. . ), in cross section of a planetarium, an locating ships (Fig.
. ), or a cooling tower for a steam or nuclear power plant. (Fig. .
Example . A semielliptical archway over a one-way road has a height of m and a width of m . The truck has a width of m and a height of . m .
Will the truck clear the opening of the archway? (Fig. . ) Since the truck’s width is3 m , to determine the clearance, we must find the height of the archway .
m from the centre. If this height is . m or less the truck will not clear the archway. From the diagram a = and b = yielding the equation of ellipse as x = .
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