Sketch the graphs of the equations
What is the relationship between these graphs? What is the eccentricity of each graph?
The graphs of the given equations are as following :-
Both the graphs are ellipse with focus at origin. One has major axis x-axis and other has y-axis.
The eccentricity of both graphs is .
We have given the following two equations :-
We have to draw the graph of these equations. We have to find the relationship between the graphs. Also we have to find the eccentricity of each graph.
The given two equations are :-
We can draw the graph of these equations as following :-
We draw the graphs of given equations as following :-
We can see that both the graphs are ellipses. The graph of ellipse has x-axis as the major axis and the graph of has y-axis as the major x-axis. The focus of both ellipses at origin.
From the graph we can see that the both equations are Ellipses.
Compare the given equations with the equation , where is the eccentricity.
The eccentricity of both ellipses 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.
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