Answer:
The polar equation for the curve represented by the given cartesian equation is [tex]r=(10c)cos(\theta)[/tex]
Step-by-step explanation:
We were given the following equation:
[tex]x^2+y^2=10cx[/tex]
and the relations between cartesian and polar coordinates are given by
[tex]x=rcos(\theta)[/tex]
[tex]y=rsin(\theta)[/tex]
where r is a radius and θ an angle. Now we replace this relations in the original cartesian equation:
[tex](rcos(\theta))^2+(rsin(\theta))^2=(10c)rcos(\theta)\Leftrightarrow r^2cos^2(\theta)+r^2sin^2(\theta)=(10cr)cos(\theta)\Leftrightarrow r^2(cos^2(\theta)+sin^2(\theta))=(10cr)cos(\theta)[/tex]
and we use that
[tex](cos^2(\theta)+sin^2(\theta))=1[/tex]
to simplify, then
[tex]r^2=(10c)rcos(\theta)\Leftrightarrow r=(10c)cos(\theta)[/tex]
wich is the polar equation for the curve.
