MA16-12 Maths Coming soon
Finding the Equation of a Tangent to a Circle
MA16-12
This lesson is coming soon.
In this lesson
Find the equation of a tangent to a circle at a given point, chaining a gradient calculation, the perpendicular-gradient rule, and rearrangement into a required format.
What it covers
- Finding the gradient of the radius from the circle's centre to the given point
- Taking the negative reciprocal of that gradient to get the tangent's gradient, using the fact that a tangent is perpendicular to the radius at the point of contact
- Using the point and the tangent gradient to find the full equation of the tangent line
- Rearranging the final answer into whatever specific format the question demands (e.g. y=mx+c or ax+by+c=0), as an explicit final checked step
Key words
For: AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | A16 | Recognise and use the equation of a circle with centre at the origin |
| Edexcel GCSE 1MA1 | A16 | Recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point |
| Eduqas GCSE C300 | HA16 | Recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point |
| OCR GCSE J560 | 7.01f | Recognise and use the equation of a circle with centre at the origin. |
| OCR GCSE J560 | 7.02b | Identify and find equations of parallel lines. |
For teachers
This GCSE Maths lesson teaches finding the equation of a tangent to a circle. By the end, students should be able to find the equation of a tangent to a circle at a given point, chaining a gradient calculation, the perpendicular-gradient rule, and rearrangement into a required format. It works through two worked examples and the mistakes examiners report.