Answer:
The polar equation of the curve is:
[tex]r=8c*cos(\theta)[/tex]
Step-by-step explanation:
In polar form x and y could be written as:
[tex]x=rcos(\theta)[/tex]
[tex]y=rsin(\theta)[/tex]
Taking the square of each value we have:
Let's recall that [tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]
[tex]x^{2}+y^{2}=r^{2}(cos^{2}(\theta)+sin^{2}(\theta))[/tex]
[tex]x^{2}+y^{2}=r^{2}[/tex]
Then, the cartesian equation is rewritten as:
[tex]x^{2}+y^{2}=8cx[/tex]
[tex]r^{2}=8c*rcos(\theta)[/tex]
Therefore, the polar equation of the curve is:
[tex]r=8c*cos(\theta)[/tex]
I hope it helps you!
