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O LevelAdditional MathsCambridgeExam QuestionsCoordinate GeometryCoordinate Geometry of the Circle

Coordinate Geometry of the Circle (Cambridge O Level Additional Maths)

Exam Questions

24 mins4 questions
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1a
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Construct the graph of space x squared space plus space y squared equals space 9

q2a-medium-2-18-equation-of-circle-edexcel-gcse-maths

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1b
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By drawing the line x space plus space y space equals space 1 on the grid, solve the equations x squared space plus space y squared space equals space 9 x space plus space y space equals 1

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2a
Sme Calculator2 marks

On the grid, construct the graph of space x squared space plus space y squared space equals space 16

q3a-medium-2-18-equation-of-circle-edexcel-gcse-maths

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2b
Sme Calculator3 marks

Find estimates for the solutions of the simultaneous equations

table row cell x squared space plus space y squared space end cell equals cell space 16 end cell row cell y space end cell equals cell space 2 x space plus 1 end cell end table

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1a
Sme Calculator5 marks

Solutions to this question by accurate drawing will not be accepted.
A circle has equation space x squared space plus space y squared space – space 16 x space – space 10 y space plus space 73 space equals space 0 space.

(i)
Find the coordinates of the centre of the circle and the length of the radius.

(ii)
Hence show that the point (10, 6.5) lies inside the circle.

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1b
Sme Calculator1 mark

A different circle has equation space left parenthesis x space – space 10 right parenthesis squared space plus space left parenthesis y space – space 6.5 right parenthesis squared space equals space 2.25 space.
Show that the two circles touch. You are not required to find the coordinates of the common point.

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1
Sme Calculator8 marks

A circle has a centre left parenthesis 2 comma space – space 4 right parenthesis and radius 3.
The linespace y space equals space 2 x space – space 3 space intersects the circle at points A and B.
The perpendicular bisector of line A B intersects the circle at points X and Y.
Find the area of kite A X B Y.

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