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You've learned how to write the equation of a circle centred at the origin.	FIGURE 1
How would we write the equation of a circle whose centre is a point other than the origin?
We will follow the same procedure as before to come up with the equation for a circle with radius r whose centre is now any point (h, k) on the coordinate plane.
The distance, d, between the centre (h, k) and any point (x, y) on the circle is computed by: d = Ö _______________ (x - h)2 + (y - k)2 = [(x - h)2 + (y - k)2]½
Since the distance between the centre (h, k) and any point (x, y) on the circle is the radius, r, we again use the distance formula to arrive at the equation: Ö _______________ (x - h)2 + (y - k)2 = r.
Squaring both sides of the equation we get (x - h)2 + (y - k)2 = r2. This is called the standard form of an equation of a circle with centre (h, k) and radius r. Sometimes this form is called the centre-radius form because the centre and radius of the circle can be easily found from this equation.
How can this be derived using the Pythagorean Theorem?
Notice that when the circle is centred at (0, 0) we get back the equation x2 + y2 = r2.
Use the standard form of the equation to answer the following questions.