2025 TKSS PRELIMS P2 Q10

2025 TKSS PRELIMS P2 Q10

Secondary 4
10 marks
2025 Tanjong Katong Secondary School Prelims A Math Paper 2

A circle has centre \(A(2, -3)\) and radius \(\sqrt{20}\).

  1. Write the equation of this circle.[1]
  2. Find the equations of the tangents to the circle that are horizontal.[2]

The circle intersects the \(y\)-axis at points \(S\) and \(T\).

  1. Find the length of \(ST\).[3]

A second circle with centre \(B\) also passes through \(S\) and \(T\).

  1. Explain why the \(y\)-coordinate of \(B\) is \(-3\).[2]
  2. Given that the \(x\)-coordinate of \(B\) is positive and that the radius of the second circle is \(\sqrt{52}\), find the \(x\)-coordinate of \(B\).[2]

Solution:

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Answer:(a) \((x-2)^2+(y+3)^2=20\) (b) \(y=-3\pm\sqrt{20}\) (c) \(ST=8\) (d) \(y_B=-3\) (e) \(x_B=6\)

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