The radius is any line segment that joins the centre of a circle to its edge.

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.

Finding the equation of a radius of a circle

Maths

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

Real-life graphs

In the equation of this circle $$(x-a)^2+(y-b)^2=r^2$$ the value of $$r$$ affects the __________ of the circle.

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.

Match the coordinate pairs for the centre of each circle to the correct equation for that circle.

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?

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 $$y=mx+c$$

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?

The radius is any __________ that joins the centre of a circle to its edge.

What is the gradient of the line passing through coordinate pairs $$(-11,11)$$ and $$(21,-53)$$?

What is the gradient of the line passing through coordinate pairs $$(-11,11)$$ and $$(21,-125)$$?

What is the equation of the line passing through coordinate pairs $$(-10,-57)$$ and $$(15,68)$$?

Which of the below equations will form a circle?

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