. . Hyperbola 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 = . Fig. .
. - - Two Dimensional Analytical Geometry - II The edge of the m wide truck corresponds to x m = . from centre We will find the height of the archway . m from the centre by substituting x = .
and solving for y + y = y = = ) = y = = = Thus the height of arch way . m from the centre is approximately2 m . Since the truck’s height is . m , the truck will clear the archway.
Example . The maximum and minimum distances of the Earth from the Sun respectively are km and . × km. The Sun is at one focus of the elliptical orbit.
Find the distance from the Sun to