The lines $y = 9$, $y = -1$ and $3y = 4x + 9$ are tangents to a circle. The $x$-coordinate o

Question

The lines $y = 9$, $y = -1$ and $3y = 4x + 9$ are tangents to a circle. The $x$-coordinate of the centre of the circle is positive. Explain why the $y$-coordinate of the centre of the circle is $4$.[1] By considering the discriminant, or otherwise, show that the $x$-coordinate of the centre of the circle is $7$.[7] Determine if the point $ (3,0) $ lies within the circle.[2]

Accepted Answer

(a) $4$ (b) $7$ (c) $\left(3,0\right)$ lies outside the circle.

2025 DSS PRELIMS P2 Q10

2025 DSS PRELIMS P2 Q10

Solution:

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