Chapter 9: Q. 43 (page 772)
Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.
Short Answer
The equation is.
Chapter 9: Q. 43 (page 772)
Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.
The equation is.
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Get started for freeIn Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar 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 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
The entire limacon
In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
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