Grades / Grade 12
Analytical Geometry: Circles
This CAPS-aligned course focuses on circles that are not centred at the origin. We will discuss the equation of a circle in centre-radius form and in general or standard form. We will look at how to complete the square to change from general form to centre-radius form. We then discuss points on a circle, and whether they lie inside, on or outside the circle. We will also study the point of intersection of a line and a circle. Tangents and circles are a very important aspect of analytical geometry and will be discussed in detail.
Lesson 1 60 minutes with Leigh on Tuesday, 10 May 2022, 17:00
Examining the equation of a circle, how to determine the coordinates at the centre and the length of the radius.
Lesson 2 60 minutes with Leigh on Thursday, 12 May 2022, 17:00
Changing the general form to centre-radius form by completing the square.
Lesson 3 60 minutes with Leigh on Tuesday, 17 May 2022, 17:00
Determining whether a point lies inside, on or outside a circle.
Lesson 4 60 minutes with Leigh on Thursday, 19 May 2022, 17:00
Solving simultaneously to determine points of intersection.
Lesson 5 60 minutes with Leigh on Tuesday, 24 May 2022, 17:00
Determining the equation of a tangent.
Lesson 6 60 minutes with Leigh on Thursday, 26 May 2022, 17:00
Consolidation of this course and working through exam-type questions.