Goals and Objectives of the
Circle Module

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 x2 + y2 = r2 write the standard equation for a circle centred at any coordinates (h, k) as (x - h)2 + (y - k)2 = r2 vary the x coordinate h in the standard equation (x - h)2 + (y - k)2 = r2 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 = r2 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 = r2 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 x2 + y2 = P in order for a circle to exist. describe that the equation x2 + y2 = P, with P = 0, describes a point. rewrite the standard equation of a circle into the form Ax2 + Ay2 + Cx + Dy + F = O. rewrite an equation of the form Ax2 + Ay2 + Cx + Dy + F = 0 into standard form (x - h)2 + (y - k)2 = r2 by completing the square. show that the standard equation of a circle is equal to the general circle equation Ax2 + Ay2 + Cx + Dy + F = 0. describe that F must be less than 0 in the general circle equation of the form x2 + y2 + F = 0 in order for a circle to exist. explain why the coefficients of x2 and y2 must be the same in the general circle equation Ax2 + Ay2 + Cx + Dy + F = 0.