IGCSEFurther MathsCambridge (CIE)Additional MathsExam QuestionsCoordinate GeometryCoordinate Geometry of the Circle

Coordinate Geometry of the Circle (Cambridge (CIE) IGCSE Additional Maths): Exam Questions

Exam code: 606

41 mins6 questions
Medium
Hard
Very Hard
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
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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
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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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2a1 mark

The circle C subscript 1 has a centre at open parentheses 3 comma space 4 close parentheses and a radius of 3.

Write down the equation of C subscript 1.

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2b7 marks

The circle C subscript 2 has the equation

x squared plus y squared minus 12 x minus 16 y plus 100 minus k squared equals 0

where k greater than 0.

Given that C subscript 2 is tangent to C subscript 1, find the value of k in each of the following cases:

(i) The circles touch each other once and neither circle lies inside the other.

(ii) The circles touch each other once and C subscript 1 lies inside C subscript 2.

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2c1 mark

A different circle, C subscript 3, intersects C subscript 1 at two distinct points, one of which has the coordinates open parentheses w comma space 7 close parentheses.

The equation of the common chord to C subscript 1 and C subscript 3 is x plus y equals 10.

Find w.

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3a4 marks

The point P open parentheses 8 comma space 8 close parentheses lies on the circle open parentheses x minus 2 close parentheses squared plus y squared equals 100 with centre C.

The circle and the tangent to the circle at P are shown below.

A circle with a tangent shown at the point P in the top right of the circle.

Find the equation of the tangent to the circle at P, giving your answer in the form y equals m x plus c.

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3b4 marks

The tangent intersects the y-axis at the point Q.

Find the area of triangle P C Q.

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1
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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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