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Sagot :
We have the equation:
[tex]r=6\cdot\cos (\theta)[/tex]And we want to write in rectangular coordinates, this is (x, y).
To do this, we need a change of variables. WE know that:
[tex]\begin{gathered} x=r\cos (\theta) \\ y=r\sin (\theta) \\ So,r^2=x^2+y^2 \end{gathered}[/tex]So our equation can be written as:
[tex]\begin{gathered} r=6\cdot\cos (\theta) \\ r^2=6r\cos (\theta) \\ \text{and replacing x and y from above} \\ x^2+y^2=6x \end{gathered}[/tex]Now, we can write the above result as:
[tex]\begin{gathered} x^2+y^2=6x \\ x^2-6x+y^2=0 \\ (x^2-6x+9-9)+y^2=0 \\ (x-3)^2-9+y^2=0 \\ (x-3)^2+y^2=9 \end{gathered}[/tex]
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