



 
Hi Michelle, Pythagoras theorem is what you need here. Suppose that a point (x, y) is on the circle then you can form a right triangle CAB as in the diagram. I chose a point in the second quadrant so y is positive but x is negative. Since the diameter of the circle is 12 its radius is 6 and hence the length CA of the line segment form C to A is 6 units. Since y is positive AB = y. But x is negative so BC = x. [For example if x = 4 then BC = (4) = 4.] Pythagoras theorem for triangle CAB says
or
This is an equation that relates x and y is (x, y) is in the second quadrant. What if (x, y) is in the first quadrant? The third quadrant? The fourth quadrant? Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 