Question) Find the equation in polar coordinates of the circle with center at the point (1,0) and which passes through the origin.
What I did first was write the equation as (x+1)^2 + (y)^2 = r^2 and since the circle passes through the origin, I substituted x and y as 0 and ended up getting the value of the radius as 1. I'm not sure how to proceed
HINT So now your circle has the equation $$(x+1)^2 + y^2 = 1.$$
You can expand $(x+1)^2$ and note that $x^2+y^2 = r^2$ while $x = r\cos \theta$. What do you get?