   SEARCH HOME Math Central Quandaries & Queries  Question from Michelle, a student: Write and equation for the circle with a center, (0,0) and a diameter of 12 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

|AB|2 + |BC|2 = |CA|2

or

y2 + (-x)2 = 62.

Thus

x2 + y2 = 62.

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.