After completing this module you will be able to: 
 describe that a circle is the set of all points equidistant from another point.

 use both the Distance Formula and the Pythagorean Theorem to derive the standard equation of a circle.

 describe a unit circle as a circle with the centre at the origin and a radius of 1 unit.

 write the standard equation for a circle centred at the origin as x^{2} +
y^{2} =
r^{2}

 write the standard equation for a circle centred at any coordinates
(h, k) as (x  h)^{2} + (y  k)^{2} = r^{2}

 vary the x coordinate h in the standard equation (x  h)^{2} + (y  k)^{2} = r^{2} to make a circle move left and right on the coordinate plane.

 vary the y coordinate k in the standard equation (x  h)^{2} + (y  k)^{2} = r^{2} to make a circle move up and down on the coordinate plane.

 vary the values of r in the standard equation (x  h)^{2} + (y  k)^{2} = r^{2} to increase and decrease the size of the circle.

 use the centre coordinates and radius of a circle to write the standard equation of a circle.

 use the standard equation of a circle to describe the centre and radius of a circle.

 describe that P must be greater than 0 in the standard equation x^{2} + y^{2} = P in order for a circle to exist.

 describe that the equation x^{2} + y^{2} = P, with P = 0, describes a point.

 rewrite the standard equation of a circle into the form Ax^{2} + Ay^{2} + Cx + Dy + F = O.

 rewrite an equation of the form Ax^{2} + Ay^{2} + Cx + Dy + F = 0
into standard form (x  h)^{2} + (y  k)^{2} = r^{2} by completing the square.

 show that the standard equation of a circle is equal to the general circle equation Ax^{2} + Ay^{2} + Cx + Dy + F = 0.

 describe that F must be less than 0 in the general circle equation of the form x^{2} + y^{2} + F = 0 in order for a circle to exist.

 explain why the coefficients of x^{2} and y^{2} must be the same in the general circle equation Ax^{2} + Ay^{2} + Cx + Dy + F = 0.
