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Chapter 6: Problem 4
The concept of ___________ is used to measure the ovalness of an ellipse.
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In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$y^{3}=x^{2}$$
A quarterback releases a pass at a height of 7 feet above the playing field, and a receiver catches the football at a height of 4 feet,30 yards directly downfield. The pass is released at an angle of \(35^{\circ}\) with the horizontal. (a) Write a set of parametric equations for the path of the football. (See Exercises 93 and 94 .) (b) Find the speed of the football when it is released. (c) Use a graphing utility to graph the path of the football and approximate its maximum height. (d) Find the time the receiver has to position himself after the quarterback releases the football.
In Exercises \(117-126\), convert the polar equation to rectangular form. Then sketch its graph. $$\theta=\pi / 6$$
Think About It The equation \(x^{2}+y^{2}=0\) is a degenerate conic. Sketch the graph of this equation and identify the degenerate conic. Describe the intersection of the plane and the double-napped cone for this particular conic.
In Exercises \(129-132,\) determine whether the statement is true or false. Justify your answer. If \(\left(r_{1}, \theta_{1}\right)\) and \(\left(r_{2}, \theta_{2}\right)\) represent the same point in the polar coordinate system, then \(\left|r_{1}\right|=\left|r_{2}\right|\).
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