Chapter 9: Q.14 (page 721)
Show that the parametrization for has the same graph as the one we plotted point by point in the reading.
Short Answer
The required parameterization of the curves traces exactly the same curve as that of the equations .
Chapter 9: Q.14 (page 721)
Show that the parametrization for has the same graph as the one we plotted point by point in the reading.
The required parameterization of the curves traces exactly the same curve as that of the equations .
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Get started for freeMeasurements indicate that Earth’s orbital eccentricity is and its semimajor axis is astronomical units.
(a) Write a Cartesian equation for Earth’s orbit.
(b) Give a polar coordinate equation for Earth’s orbit, assuming that the sun is the focus of the elliptical orbit.
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
Three noncollinear points determine a unique circle. Do three noncollinear points determine a unique ellipse? If so, explain why. If not, provide three noncollinear points that are on two distinct ellipses.
Use polar coordinates to graph the conics in Exercises 44–51.
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
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