Unit circle
A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle. The unit circle is very useful in Trigonometry.
(b) x^{2}+ ( y - 3)^{2 } = 4
In this part, it looks as the x coordinate of the center is zero as with the earlier part. However, this time there is something more with the y term and thus comparing this term to the standard form of the circle we can see that the y coordinate of the center have to be 3. The center & radius of this circle is then,
center = (0, 3) radius = √4 = 2
Following is a sketch of the circle. The center is marked alongwith a red cross in this graph.