Question 1102814: Identify the type of graph of the following polar equations. How can the graphs best be described?
a. rsinθ = -11
https://www.dropbox.com/s/xo8bahbd0r5qxfh/Screen%20Shot%202017-11-21%20at%209.18.13%20AM.png?dl=0
b. r = 3-2sinθ
https://www.dropbox.com/s/i99qmpa4vmrir0u/Screen%20Shot%202017-11-21%20at%209.18.23%20AM.png?dl=0
c. r^2 = 25cos2θ
https://www.dropbox.com/s/vboagd17yavux3s/Screen%20Shot%202017-11-21%20at%209.18.36%20AM.png?dl=0
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! c . You probably asked question 1102813,
and from that question you should know that the answer to part c is
a lemniscate symmetric about the origin and the x- and y-axes,
or as your answer option says, in polar coordinates,
"symmetric about the pole and the lines  and the vertical line  ."
a. As  is part of the conversion from polar to cartesian coordinates,
 translates into  ,
and represents a horizontal line.
b.  graphs ans a limacon with a dimple,
because, in absolute value, the coefficient of the trigonometric function (2)
is between 1/2 and 1 times the other term (3).
The dimple is at because that is where  is minimum.
For  ,  and  .
For  ,  and  has increased to  ,
but as we keep approaching , starts to decrease forming a dimple.
At ,  and  again.
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