About this topic
Before you begin
Use coordinate geometry for lines and circles, and linearise power and exponential relationships.
Learning goals
- Produce complete line equations and distinguish parallel, coincident, perpendicular and other intersecting lines
- Produce parallel and perpendicular line equations through a specified point
- Produce a segment midpoint and the complete perpendicular-bisector equation
- Calculate the area enclosed by an explicitly ordered coordinate polygon
- Produce a circle equation, centre and radius from its given algebraic or geometric facts
- Produce a complete tangent equation at a specified point on a single circle
- Reason and calculate using coordinate geometry
- Produce every real intersection point of one line and one circle
- Produce transformed variables and the complete symbolic straight-line coefficients
- Recover the straight-line equation and original model constants from labelled transformed graphs
Syllabus statements covered
- Condition for two lines to be parallel or perpendicular
- Midpoint of line segment
- Area of rectilinear figure
- Coordinate geometry of circles in the form:
- (x − a)² + (y − b)² = r^2
- x^2 + y^2 + 2gx + 2 fy + c = 0 (excluding problems involving two circles)
- Transformation of given relationships, including y = ax^n and y = kb^x, to linear form to determine unknown constants from a straight line graph
- Condition for two lines to be parallel or perpendicular
- Midpoint of line segment
- Area of rectilinear figure
- Coordinate geometry of circles in the form:
- (x − a)² + (y − b)² = r^2
- x^2 + y^2 + 2gx + 2 fy + c = 0 (excluding problems involving two circles)
- Transformation of given relationships, including y = ax^n and y = kb^x, to linear form to determine unknown constants from a straight line graph
Choose a lesson
Work through them in order.
- Not startedCoordinate circles and perpendicular linesNextUse perpendicular directions, midpoint and area conditions, then recover a circle and verify tangency on the original equation.
- Not startedRecover a circle and find every intersectionNextUse equal-distance conditions to recover a circle, then solve and check complete line–circle intersection sets.
- Not startedLinearise power and exponential modelsNextChoose transformed axes, recover power or exponential constants and test the model against original data and domain limits.
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