P2.3.1 - Coordinate geometry of the circle

Coordinate geometry of the circle Students should be able to find the radius and the using the equation of a circle in the coordinates of the centre of the circle, given the equation of form (x − a)2 + (y − b)2 = r2 and the circle and vice versa. including use of the following circle properties: (i) the angle in a semicircle is a right angle.; (ii) the perpendicular from the centre to a chord bisects the chord.; (iii) the perpendicularity of radius and tangent.

Use coordinate geometry of the circle to connect the rule to the data and decision in the question.

This matters because coordinate geometry of the circle determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply coordinate geometry of the circle to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Coordinate geometry of the circle is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.