Year 11 - Maths
Finding the equation of the tangent to a circle
Real-life graphs
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.
Lesson Summary
You will learn to find the equation of the tangent to a circle at any given point.
Key Notes
- Using the gradient of the radius through a given point, you can find the equation of the tangent at this same point.
- You have already proved that the tangent at any point on a circle is perpendicular to the radius at that point.
- You have already proved that the product of the gradients of two perpendicular lines is -1
- Using the gradient of the tangent and the coordinates of the point, you can find the equation of the tangent.
Vocabulary To Learn
- Gradient: The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.
- Radius: The radius is any line segment that joins the centre of a circle to its edge.
- Tangent: A tangent of a circle is a line that intersects the circle exactly once.
Common Mistakes To Avoid
- Pupils can confuse the gradient of the radius with the length of the radius.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Using the gradient of the radius through a given point, you can find the equation of the tangent at this same point. You have already proved that the tangent at any point on a circle is perpendicular to the radius at that point.
2. Use this key word in a maths sentence and explain it clearly. 'Gradient'
The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils can confuse the gradient of the radius with the length of the radius. Correction: A sketch will help pupils apply the right skills. To find the equation of a straight line we need the gradient. You may wish to draw concentric circles to show pupils that the radii are different lengths but can have same gradient.
More Lessons In This Unit
- Advanced problem solving with real-life graphs Study Guide
- Calculating journeys from linear speed-time graphs Study Guide
- Calculating the rate of change Study Guide
- Checking and securing understanding of drawing distance-time graphs Study Guide
- Checking and securing understanding of reading from context-based graphs Study Guide
- Distance-time graphs Study Guide
- Efficiently estimating journeys from non-linear graphs Study Guide
- Estimating journeys from non-linear graphs Study Guide
- Estimating the gradient of a curve Study Guide
- Finding the equation of a radius of a circle Study Guide
- Improving the estimate of the gradient of a curve Study Guide
- Interpreting and drawing more real-life graphs Study Guide
- Interpreting and drawing real-life graphs Study Guide
- Non-linear distance-time graphs Study Guide
- Problem solving with real-life graphs Study Guide
- Speed-time graphs Study Guide
Browse all guides in the Year 11 Maths guide library.