A circle is centered at the origin and has a radius of $1$. 

1. What is the equation of the circle?

   Hint (a):

   The general equation of a circle is $x^2+y^2=r^2$.

2. If $x=\frac{1}{2}$ in the equation you wrote in part (a), what is the exact value of $y$? Note: You should get two values.

   Step (b):

   $\frac{1}{4}+y^2=1$