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) x²+ ( 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.