Video lecture (English) of C12 Coordinate Geometry (II)
C12 Coordinate Geometry (II)
What’s on the Specification
| MM3.1 | Equation of a straight line, including:
Conditions for two straight lines to be parallel or perpendicular to each other. Finding equations of straight lines given information in various forms. |
| MM3.2 | Coordinate geometry of the circle, using the equation of a circle in the forms:
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| MM3.3 | Use of the following circle properties:
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Learning Objectives
- Deconstruct circle algebraic forms by translating between the expanded general form $\left(x^2+y^2+c x+d y+e=0\right)$ and the standard Cartesian form $\left((x-a)^2\right.$ $+$ $(y-b)^2$ $=$ $\left. r^2\right)$ by completing the square.
- Evaluate line-circle intersections by determining the geometric relationship between a line and a circle through algebraic discriminant analysis or the orthogonal distance from the centre to the line.
- Formulate exact tangent equations by using the axiom that a tangent is perpendicular to the radius at the point of contact to derive its equation at any given coordinate.
- Synthesise Euclidean circle theorems by integrating classical axioms—such as chord bisection, right angles in semicircles, and the alternate segment theorem—into 2D coordinate proofs and spatial mapping.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 15 | 180 min |
| Quiz | 10 | 30 min |
| Practice A | 30 | 75 min |
| Practice B | 20 | 75 min |
| Total | 75 | approx. 6-7 hrs |
Video Lecture (English):
Practice:
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