Equidistant Points and Circle Equations
●
Write down the coordinates of as many points as possible that
are equidistant from the origin?
Going in circles with Pythagoras
1
●
Write down the coordinates of as many points as possible that
are equidistant from the point (3, 2)?
●
Do these points fit into an equation? Why does this work?
2
Group Discussion
Should we be able to extend this learning to any size circle with centre
(3,2)?
How about any circle, with any centre?
Can we write an equation like this for any circle?
A
(
x
,
y
)
2
4
What is the equation of this circle with centre
c and radius 2?
c
(
3
,
2
)
c
(
h
,
k
)
B
(
x
,
y
)
r
What is the equation of this circle with centre
c and radius r?
6
Class Discussion
Summarise your learning from today’s lesson
Phase 1
Assessing Students prior knowledge with some formative assessment and an activity which should lead to a brief discussion about how to find as many points as possible using Pythagoras. Students may also use a compass which will should be encouraged.
In this engaging content, we delve into the concept of equidistant points from the origin as well as a specific point. We explore the coordinates of such points, their fitting into equations, and extending this learning to circles with various centers. Furthermore, we discuss writing equations for circles with diverse centers and radii. The class discussion wraps up by summarizing the key takeaways from the lesson.
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Presentation Transcript
Going in circles with Pythagoras Write down the coordinates of as many points as possible that are equidistant from the origin? 1
Write down the coordinates of as many points as possible that are equidistant from the point (3, 2)? Do these points fit into an equation? Why does this work? 2
Group Discussion Should we be able to extend this learning to any size circle with centre (3,2)? How about any circle, with any centre? Can we write an equation like this for any circle?
What is the equation of this circle with centre c and radius 2? A(x,y) 2 c(3,2) 4
What is the equation of this circle with centre c and radius r? B(x,y) r c(h,k)
Class Discussion Summarise your learning from today s lesson 6
