Math CentralQuandaries & 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


y2 + (-x)2 = 62.


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?


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