The polar equation of the circle of R=1

Questions
1

In1:= r^2 - 6 r Cos[[Theta]] - 4 r Sin[[Theta]] == -12

Out[1]= r^2 - 6 r Cos[\[Theta]] - 4 r Sin[\[Theta]] == -12

In[2]:= Solve[r^2 - 6 r Cos[\[Theta]] - 4 r Sin[\[Theta]] == -12, r]

Out[2]= {{r -> 
   1/2 (6 Cos[\[Theta]] + 4 Sin[\[Theta]] - 
      Sqrt[2] Sqrt[-11 + 5 Cos[2 \[Theta]] + 
        12 Sin[2 \[Theta]]])}, {r -> 
   1/2 (6 Cos[\[Theta]] + 4 Sin[\[Theta]] + 
      Sqrt[2] Sqrt[-11 + 5 Cos[2 \[Theta]] + 12 Sin[2 \[Theta]]])}}

In[5]:= PolarPlot[
 1/2 (6 Cos[\[Theta]] + 4 Sin[\[Theta]] - 
    Sqrt[2] Sqrt[-11 + 5 Cos[2 \[Theta]] + 
      12 Sin[2 \[Theta]]]), {\[Theta], 0, 2 Pi}]

re25.png
re25.png613×383 41.8 KB

2

I’m sorry. I’m not sure I understand the question. Is there something wrong with the results?

3

PolarPlot[ 1/2 (6 Cos[[Theta]] + 4 Sin[[Theta]] - Sqrt[2] Sqrt[-11 + 5 Cos[2 [Theta]] + 12 Sin[2 [Theta]]]), {[Theta], 0, 2 Pi}]

re26.png
re26.png628×105 4.15 KB

4

I see that you are posting a lot of screen shots.

I’m sorry. I’m not able to tell what the issue is from them. Can you please be explciit about what the issue is?