Chapter 10: Q43. (page 677)
In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
The equation defines hyperbola.
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To transform the equation
into one in and without an term, rotate the axes
through an acute angle that satisfies the equation _______.
If is acute, the Half-angle Formula for the sine function isrole="math" localid="1646654694239" .
Semi elliptical Arch Bridge The arch of a bridge is a semi ellipse with a horizontal major axis. The span is feet, and the top of the arch is feet above the major axis. The roadway is horizontal and is feet above the top of the arch. Find the vertical distance from the roadway to the arch at -foot intervals along the roadway.
A hyperbola for which is called an equilateral hyperbola. Find the eccentricity of an equilateral hyperbola.
[Note: The eccentricity of a hyperbola is defined in Problem 81.]
Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Focus atand its vertex at.
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