The diagram below is not drawn to scale. In the diagram, $D, E$ and $F$ are points on the circle

Question

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]

Accepted Answer

(a) Centre $= (4,-1)$ (b) $x^2 + y^2 - 8x + 2y - 17 = 0$ (c) $ (x + 8)^2 + (y + 1)^2 = 34$

2024 FMSS PRELIMS P2 Q11

2024 FMSS PRELIMS P2 Q11