Finding the equation of a radius of a circle
I can find the equation of a radius of a circle.
Finding the equation of a radius of a circle
I can find the equation of a radius of a circle.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- The equation of a circle gives the coordinates of the centre of the circle.
- Using this and the coordinates of a point on the circle, you can calculate the gradient of the radius.
- Using the gradient and the centre of the circle, you can find the equation of this radius.
Keywords
Radius - The radius is any line segment that joins the centre of a circle to its edge.
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.
Common misconception
Pupils may think that a circle with equation $$(x+a)^2 + (y+b)^2=r^2$$ has centre $$(a,b)$$
The general form of an equation of a circle is $$(x-a)^2 + (y-b)^2=r^2$$ where $$(a,b)$$ is then the centre. Graphing software will be useful to show and explore this general form.
To help you plan your year 11 maths lesson on: Finding the equation of a radius of a circle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Finding the equation of a radius of a circle, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Real-life graphs unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Starter quiz
6 Questions

Exit quiz
6 Questions
$$(3,5)$$ -
$$(x-3)^2+(y-5)^2=1$$
$$(-3,5)$$ -
$$(x+3)^2+(y-5)^2=1$$
$$(-3,-5)$$ -
$$(x+3)^2+(y+5)^2=1$$
$$(5,-3)$$ -
$$(x-5)^2+(y+3)^2=1$$
$$(5,3)$$ -
$$(x-5)^2+(y-3)^2=1$$
$$(-5,3)$$ -
$$(x+5)^2+(y-3)^2=1$$