A-Level Mathematics Revision — Coordinate Geometry
Revise Coordinate Geometry for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What is Coordinate Geometry?
Coordinate geometry at A-Level involves the study of geometric shapes and figures using coordinates. It builds on GCSE concepts by introducing more complex ideas such as the equations of circles, the properties of tangents and normals, and the use of parametric equations to describe curves.
Board notes: All major A-Level Maths boards (AQA, Edexcel, OCR) cover coordinate geometry in depth, including circles and parametric equations. The level of complexity of the problems can vary slightly between boards.
Step-by-step explanationWorked examples
Worked example
Find the equation of the circle with centre (2, -3) and radius 5. The equation of a circle is (x-a)² + (y-b)² = r², where (a,b) is the centre and r is the radius. Substituting the given values, we get (x-2)² + (y-(-3))² = 5², which simplifies to (x-2)² + (y+3)² = 25.
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Start with low-focus cards for Coordinate Geometry, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Confusing the formulae for the gradient and the length of a line segment. The gradient is the change in y divided by the change in x, while the length is found using Pythagoras' theorem.
- 2Making errors when finding the equation of a line, particularly with the use of the formula y - y1 = m(x - x1).
- 3Incorrectly identifying the centre and radius of a circle from its equation, especially when the equation is not in the standard (x-a)² + (y-b)² = r² form.
Coordinate Geometry exam questions
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Frequently asked questions
How do I find the point of intersection of two lines?
To find the point of intersection of two lines, you need to solve their equations simultaneously. This can be done by substitution or elimination.
What is a normal to a curve?
A normal to a curve at a particular point is a line that is perpendicular to the tangent at that same point. The gradient of the normal is the negative reciprocal of the gradient of the tangent.