Chapter 9: Q 30. (page 730)
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
Short Answer
The polar coordinates are , for any integer k.
Chapter 9: Q 30. (page 730)
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
The polar coordinates are , for any integer k.
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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.
Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.
Measurements indicate that the orbital eccentricity of Mars is and its semimajor axis is astronomical units.
(a) Write a Cartesian equation for the orbit of Mars.
(b) Do and have the same meaning as in Exercise 53?
(c) Give a polar coordinate equation for the orbit of Mars, assuming that the sun is the focus of the elliptical orbit.
Explain why there are infinitely many different hyperbolas with the same foci.
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