Chapter 9: Q 2 (page 774)
Sketch the curves defined by
the given sets of parametric equations. Indicate the direction
of motion on each curve.
Short Answer
The required graph is shown below:
Chapter 9: Q 2 (page 774)
Sketch the curves defined by
the given sets of parametric equations. Indicate the direction
of motion on each curve.
The required graph is shown below:
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Get started for freeIn Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
Measurements 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 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 .
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
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.
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