2024 FMSS PRELIMS P2 Q11
2024 FMSS PRELIMS P2 Q11
12 marks
The diagram below is not drawn to scale.
In the diagram, \(D, E\) and \(F\) are points on the circle \(C_1\).
- Show that \(DE\) is the diameter of the circle \(C_1\) and hence find the centre of \(C_1\).[5]
- Find the equation of the circle \(C_1\) in the form \(x^2 + y^2 + px + qy + r = 0\), where \(p\), \(q\) and \(r\) are integers.[3]
- Given that the circle \(C_2\) is a reflection of the circle \(C_1\) in the line \(x = -2\), find the equation of \(C_2\).[2]
- Explain why point \((3, 4)\) lies within only one of the circles \(C_1\) and \(C_2\).[2]
Solution:
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Answer:(a) \(DE\) is a diameter (shown); centre \((4,-1)\). (b) \(x^2+y^2-8x+2y-17=0\). (c) \((x+8)^2+(y+1)^2=34\). (d) Squared distances \(26<34\) and \(146>34\): within \(C_1\) only.
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