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Chapter 9: Q. 26 (page 747)
Graph the equations in Exercises 25鈥�32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17鈥�24 .
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Show that the eccentricity satisfies the equation.
In Exercises 60 and 61 we ask you to prove Theorem 9.23 for ellipses and hyperbolas
Consider the ellipse with equation where . Let be the focus with coordinates . Let and l be the vertical line with equation . Show that for any point P on the ellipse, , where is the point on closest to .
Sketch the graphs of the equations
and
What is the relationship between these graphs? What is the eccentricity of each graph?
Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression
The integral is
Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.
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