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Chapter 7: Problem 5
Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$y^{2}=16 x$$
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Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. $$\left\\{\begin{array}{c}4 x^{2}+y^{2}=4 \\\x+y=3\end{array}\right.$$
Convert each equation to standard form by completing the square on \(x\) or \(y .\) Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$y^{2}-2 y+12 x-35=0$$
Graph \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) and \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1\) in the same viewing rectangle for values of \(a^{2}\) and \(b^{2}\) of your choice. Describe the relationship between the two graphs.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. What happens to the shape of the graph of \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) as \(\frac{c}{a} \rightarrow \infty,\) where \(c^{2}=a^{2}+b^{2} ?\)
The towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280 meters apart and rise 160 meters 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 200 meters from a tower? Round to the nearest meter. (Image can't copy)
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