﻿Hi, I'm Miss Davies. In this lesson, we're going to be looking at whether a point lies on, outside, or inside of a circle. All of these points lie on this circle. What pattern do they follow? If we look at the x and y coordinates, we can see that the sum of the squares of both the x and the y values add to make 25. This is because the radius squared is 25. For a point to lie on a circle, it must satisfy the equation of the circle. The equation of this circle is x squared add y squared is equal to 25. If we consider the point three, three, visually, we can see that that point lies within the circle, but if we aren't give the diagram, we are only given the equation and the coordinate, we can substitute in the values for x and y to give three squared add three squared. This gives us 18. Since 18 is less than the radius squared of 25, the point three, three lies inside the circle. The equation of the circle is x squared add y squared is equal to 25. If we consider a point four, negative four, we can see from the diagram that that lies outside of the circle. We can substitute the values for x and y into the equation x squared add y squared. This gives 32. Since 32 is greater than 25, the point lies outside of the circle. In this next example, we have been given the equation of a circle and we must decide whether each point lies on, inside, or outside of this circle. We aren't going to draw a sketch to help us with these questions. If we look at the coordinate 10, negative eight, the x value is 10 and the y value is negative eight. If we substitute these values into x squared add y squared, it gives us an answer of 164. 164 is greater than 36, so this point lies outside of the circle. With our next example, the coordinate zero, six, if we substitute these values into the equation, it gives the result of 36. This is the radius of the circle squared. So the point lies on the circle. With our final example, our x value is negative three and our y value is negative five. If we substitute these two values into the equation, it gives us a result of 34. 34 is less than 36, so this point lies inside of the circle. Here are some questions for you to try. Pause the video to complete your task and resume once you're finished. Here are the answers. The points negative six, eight and zero, negative 10 both lie on the circle, as the values satisfy the equation. Here are some questions for you to try. Pause the video to complete your task and resume once you're finished. Here are the answers. There are more than one correct answer for all but one of these gaps. Here are some questions for you to try. Pause the video to complete your task and resume once you're finished. Here are the answers. The point four, nine lies outside of the circle x squared add y squared is equal to 25, as four squared add nine squared is equal to 97, and 97 is greater than 25. The point negative seven, zero lies inside of the circle x squared add y squared is equal to 20, as seven squared add zero squared is 49, and 49 is less than 50. The point nine, negative one lies outside of the circle x squared add y squared is equal to 80, as nine squared add negative one squared is 82, and 82 is greater than 80. We have been asked to find the equation of the circle that has a centre of zero, zero, that the point negative six, negative two lies on. Because the centre of the circle is zero, zero, we know that the equation is going to be x squared add y squared equals the radius squared. If we substitute in our values for x and y from the coordinate, we get a result of 40. This means that the radius squared is 40. The equation of the circle is going to be x squared add y squared is equal to 40. Here is a question for you to try. Pause the video to complete your task and resume once you're finished. Here is the answer. Negative four squared add two squared is equal to 20. This gives the equation x squared add y squared is equal to 20. That's all for this lesson. Thanks for watching.

In this lesson, we will use substitution to decide whether a point lies outside or inside a circle.

Maths

Y11 Maths (Higher)

Key Stage 4

Year 11

Miss

Decide whether a point lies, on, outside or inside a circle

Circle Graphs

Algebra (A)

THEME

UNIT

Draw and recognise circle graphs of the form x² + y² = r²

Intersection of lines and circles

Find the equation of a tangent to a circle at a given point

Lesson overview:Decide whether a point lies, on, outside or inside a circle

Core Content

Circle Graphs: