Question

How do you turn r=6costheta into a rectangular equation ?

Answer 1

We have the equation:

`r=6\cdot\cos (\theta)`

And we want to write in rectangular coordinates, this is (x, y).

To do this, we need a change of variables. WE know that:

`\begin{gathered} x=r\cos (\theta) \\ y=r\sin (\theta) \\ So,r^2=x^2+y^2 \end{gathered}`

So our equation can be written as:

`\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}`

Now, we can write the above result as:

`\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}`