$A(1, 7)$ and $B(9, 7)$ lie on a circle $C_1$ with centre $P$. The line $4y + 3x = 31$ is

Question

$A(1, 7)$ and $B(9, 7)$ lie on a circle $C_1$ with centre $P$. The line $4y + 3x = 31$ is a normal to the circle and passes through $A$. Use a geometrical property of circle to explain why the $x$-coordinate of $P$ is $5$.[2] Find the equation of the circle $C_1$ The tangent to the circle at A intersects the y-axis at D. Find the coordinates of D. A larger circle $C_2$ has the same centre P and radius three times that of $C_1$. T is a point on $C_2$ such that P,A and T are collinear and the x-coordinates of T is negative. Determine the coordinates of T.

Accepted Answer

(ii)Equation of circle : $(x-5)^2+(y-4)^2=25$ (iii)$D : (0,\frac{17}{3})$ (iv)$T:(-7,13)$

2025 CHS PRELIMS P2 Q10

2025 CHS PRELIMS P2 Q10