Chapter 9: Q. 34 (page 772)
Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
Short Answer
The equation is
Chapter 9: Q. 34 (page 772)
Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
The equation is
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Get started for freeConsider the hyperbola with equation Let F be the focus with coordinates Let and l be the vertical line with equation Show that for any point P on the hyperbola, where D is the point on l closest to P.
Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.
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
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.
in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
One petal of the polar rose
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