Exam 10: Parametric Equations and Polar Coordinates

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Find an equation for the conic section with the given properties. All points such that the difference of the distances to the points (-5, 27) and (-5, -13) equals 24

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Plot the given polar point. Plot the given polar point.    Plot the given polar point.

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Find a polar equation for the conic section with focus Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix    and the given directrix and eccentricity. Directrix Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix    Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix

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Identify all values of Identify all values of   where r = 0.  where r = 0. Identify all values of   where r = 0.

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Plot the given polar point. Plot the given polar point.    Plot the given polar point.

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Find the slope of the tangent line to the polar curve at the given point. Find the slope of the tangent line to the polar curve at the given point.

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Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)    Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

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Interpret and graph the conic section. Interpret and graph the conic section.

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Find a polar equation for the conic section with focus Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix    and the given directrix and eccentricity. Directrix Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix    Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix

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Which of the following sets of parametric equations is equivalent to Which of the following sets of parametric equations is equivalent to   ? ?

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Find parametric equations describing the given curve. The line segment from Find parametric equations describing the given curve. The line segment from   to  to Find parametric equations describing the given curve. The line segment from   to

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Find all polar coordinate representations of the given rectangular point. Find all polar coordinate representations of the given rectangular point.

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Sketch the plane curve defined by the given parametric equations. Sketch the plane curve defined by the given parametric equations.    Sketch the plane curve defined by the given parametric equations.

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Find all points at which the two curves intersect. Find all points at which the two curves intersect.   and  and Find all points at which the two curves intersect.   and

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Which of the following sets of parametric equations is equivalent to Which of the following sets of parametric equations is equivalent to   ? ?

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A parabolic reflector is used by a sports broadcast engineer to amplify the conversations between football players on the field. If the reflector has the shape x = 4y2, where should the microphone be placed?

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The time required for a skier, initially at rest, to ski from point A to point B on an inclined plane (where B is not directly downhill from A ) 6.6855k

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Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

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Graph the conic section with focus Graph the conic section with focus   and the given directrix and eccentricity. Directrix    and the given directrix and eccentricity. Directrix Graph the conic section with focus   and the given directrix and eccentricity. Directrix    Graph the conic section with focus   and the given directrix and eccentricity. Directrix

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For the given parametric equations, find a corresponding x-y equation for the curve. For the given parametric equations, find a corresponding x-y equation for the curve.

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