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Chapter 10: Problem 75
Describe how to locate the foci for \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)
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Find the standard form of the equation of an ellipse with vertices at \((0,-6)\) and \((0,6),\) passing through \((2,-4)\)
Use a graphing utility to graph the equation. Then answer the given question. Use the polar equation for planetary orbits, $$ r=\frac{\left(1-e^{2}\right) a}{1-e \cos \theta} $$ to find the polar equation of the orbit for Mercury and Earth. Mercury: \(e=0.2056\) and \(a=36.0 \times 10^{6}\) miles Earth: \(\quad e=0.0167\) and \(a=92.96 \times 10^{6}\) miles Use a graphing utility to graph both orbits in the same viewing rectangle. What do you see about the orbits from their graphs that is not obvious from their equations?
a. Identify the conic section that each polarequation represents. b. Describe the location of a directrix from the focus located at the pole. $$ r=\frac{8}{2-2 \sin \theta} $$
The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 100 feet from a tower?
In Exercises \(67-68,\) graph each semiellipse. $$ y=-\sqrt{4-4 x^{2}} $$
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