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You've learned that x2 + y2 = r2 is the equation in standard form for a circle centred at the origin with radius r.

Now what if we replace the r2 in the equation with a real number denoted by P, where P can be positive, negative or zero.

Use the action figure to explore the following question: For what values of of P does the equation x2 + y2 = P describe a circle?

Once you've done this, use the following questions to check your understanding of the effect that the value of P has on the circle.

It follows nicely that x2 + y2 = P yields a circle only when P is positive, because it is only when P is positive that we can find a real number r such that r2 = P.

Now lets explore another special form of the circle equation.