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Chapter 10: Q52. (page 677)
In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
The equation defines ellipse.
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In Problems 31– 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40.
To transform the equation
into one in and without an term, rotate the axes
through an acute angle that satisfies the equation _______.
In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river meters wide. The center of the arch is meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.
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