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avatar+221 

Which conic section is represented by the polar equation r= 1/3+3sinθ

 

hyperbola

parabola 

circle 

ellipse 

quilly  Mar 28, 2018
 #1
avatar+92723 
+3

r  =      1  / [3 + 3 sin θ]

 

3r  =  1 / [ 1 + sinθ]

 

3r  =  1 / [ 1  +  y /r]

 

3r  =  r /  [ r + y]

 

r + y  =  1/3

 

r  =  (1/3)  - y

 

√[x^2 + y^2]  =  (1/3) - y       square both sides

 

x^2  + y^2   =  1/9  - (2/3)y + y^2

 

x^2  =  1/9 - (2/3)y

 

9x^2 =  1  + 6y

 

6y  =   -9x^2 + 1

 

y  = (-3/2)x^2  + 1/6

 

This is a parabola  ...  see  here  :  https://www.desmos.com/calculator/m0v1m8zsrd

 

 

cool cool cool

CPhill  Mar 28, 2018
 #2
avatar+94106 
+2

Nice work Chris!

 

Quilly, if this is what you intended, and I expect it is, then you need to learn to use BRACKETS

I read it as you had written it which is     y=     1/3     +    3sin(theta)

And so there is no way I could have given this answer!

 

You are lucky that CPhill has been practicing his forensic mathematics!

Melody  Mar 28, 2018
 #3
avatar+221 
+6

Goodness, I'm sorry about that.

quilly  Mar 28, 2018
 #4
avatar+92723 
0

Thanks  ....!!!!

 

 

cool cool cool

CPhill  Mar 28, 2018

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