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Year 11
Higher

Finding the equation of a radius of a circle

I can find the equation of a radius of a circle.

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New
New
Year 11
Higher

Finding the equation of a radius of a circle

I can find the equation of a radius of a circle.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The equation of a circle gives the coordinates of the centre of the circle.
  2. Using this and the coordinates of a point on the circle, you can calculate the gradient of the radius.
  3. 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.

A recap of completing the square may be helpful for some pupils so they can rearrange circle equations confidently. Graphing software is going to help pupils check and explore the concepts in all stages of this lesson.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
The radius is any __________ that joins the centre of a circle to its edge.
diameter
Correct answer: line segment
arc
chord
circumference
Q2.
What is the gradient of this line?
An image in a quiz
Correct Answer: 6
Q3.
What is the gradient of the line passing through coordinate pairs $$(-11,11)$$ and $$(21,-53)$$?
Correct Answer: -2
Q4.
What is the gradient of the line passing through coordinate pairs $$(-11,11)$$ and $$(21,-125)$$?
$${{32}\over{-136}}$$
Correct answer: $${{-17}\over{4}}$$
$${{-32}\over{136}}$$
$${{17}\over{4}}$$
$${{-4}\over{17}}$$
Q5.
What is the equation of the line passing through coordinate pairs $$(-10,-57)$$ and $$(15,68)$$?
Correct answer: $$y=5x-7$$
$$y=5x+7$$
$$y=7 - 5x$$
$$y=-5x-107$$
$$y=5x+107$$
Q6.
Which of the below equations will form a circle?
$$x^2+y=9^2$$
Correct answer: $$x^2+y^2=9$$
$$x^2-y^2=9$$
Correct answer: $$x^2+y^2=9^2$$
$$(x+y)^2=9$$

Exit quiz

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6 Questions

Q1.
In the equation of this circle $$(x-a)^2+(y-b)^2=r^2$$ the value of $$r$$ affects the __________ of the circle.
Correct answer: radius
ratio
range
rate of change
centre
Q2.
In the equation of this circle $$(x-a)^2+(y-b)^2=r^2$$ the values of $$a$$ and $$b$$ affect the __________ of the circle.
chord
circumference
radius
diameter
Correct answer: centre
Q3.
Match the coordinate pairs for the centre of each circle to the correct equation for that circle.
Correct Answer:$$(3,5)$$,$$(x-3)^2+(y-5)^2=1$$

$$(x-3)^2+(y-5)^2=1$$

Correct Answer:$$(-3,5)$$,$$(x+3)^2+(y-5)^2=1$$

$$(x+3)^2+(y-5)^2=1$$

Correct Answer:$$(-3,-5)$$,$$(x+3)^2+(y+5)^2=1$$

$$(x+3)^2+(y+5)^2=1$$

Correct Answer:$$(5,-3)$$,$$(x-5)^2+(y+3)^2=1$$

$$(x-5)^2+(y+3)^2=1$$

Correct Answer:$$(5,3)$$,$$(x-5)^2+(y-3)^2=1$$

$$(x-5)^2+(y-3)^2=1$$

Correct Answer:$$(-5,3)$$,$$(x+5)^2+(y-3)^2=1$$

$$(x+5)^2+(y-3)^2=1$$

Q4.
What is the gradient of the radius connecting the centre of the circle $$(x-8)^2+(y-2)^2=10$$ to the point $$(9,5)$$ on the circumference?
Correct answer: $$3$$
$$1\over3$$
$$-1\over3$$
$$-3$$
Q5.
What is the equation of the radius connecting the centre of the circle $$(x+5)^2+(y-3)^2=5$$ to the point $$(-4,5)$$ on its circumference? Write your answer in the form $$y=mx+c$$
Correct Answer: y=2x+13, y = 2x + 13
Q6.
What is the equation of the radius connecting the centre of the circle $$(x+5)^2+(y+8)^2=20$$ to the point $$(-1,-6)$$ on its circumference?
Correct answer: $$y={1\over2}x-{11\over2}$$
$$y=-{1\over2}x-{11\over2}$$
$$y={1\over2}x+{11\over2}$$
$$y={1\over2}x-{2\over11}$$
$$y=2x-{11\over2}$$