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Chapter 6: Problem 30
Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Vertical axis and passes through the point (-3,-3)
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Describe in words how a plane could intersect with the double-napped cone shown to form the conic section. Hyperbola
Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are 1280 meters apart. The top of each tower is 152 meters above the roadway. The cables touch the roadway midway between the towers. (a) Draw a sketch of the bridge. Locate the origin of a rectangular coordinate system at the center of the roadway. Label the coordinates of the known points. (b) Write an equation that models the cables. (c) Complete the table by finding the height \(y\) of the suspension cables over the roadway at a distance of \(x\) meters from the center of the bridge. $$\begin{array}{|c|c|}\hline \text { Distance, } \boldsymbol{x} & \text { Height, } \boldsymbol{y} \\\\\hline 0 & \\\100 & \\\250 & \\\400 & \\\500 & \\\\\hline\end{array}$$
Halley's comet has an elliptical orbit, with the sun at one focus. The eccentricity of the orbit is approximately 0.967 . The length of the major axis of the orbit is approximately 35.88 astronomical units. (An astronomical unit is about 93 million miles.) (a) Find an equation of the orbit. Place the center of the orbit at the origin, and place the major axis on the \(x\) -axis. (b) Use a graphing utility to graph the equation of the orbit. (c) Find the greatest (aphelion) and smallest (perihelion) distances from the sun's center to the comet's center.
Use a graphing utility to graph the polar equation. Describe your viewing window. \(r=\frac{5 \pi}{8}\)
You and a friend live 4 miles apart (on the same "east-west" street) and are talking on the phone. You hear a clap of thunder from lightning in a storm, and 18 seconds later your friend hears the thunder. Find an equation that gives the possible places where the lightning could have occurred. (Assume that the coordinate system is measured in feet and that sound travels at 1100 feet per second.)
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