The diagram shows part of the curve $y = \frac{5}{x}$, $y = \pi$ and $x = \frac{3\pi}{2}$. The

Question

The diagram shows part of the curve $y = \frac{5}{x}$, $y = \pi$ and $x = \frac{3\pi}{2}$. The curve $y = \frac{5}{x}$ cuts the line $y = \pi$ at $P$ and cuts the line $x = \frac{3\pi}{2}$ at $Q$. Find the coordinates of $P$ and of $Q$ in terms of $\pi$.[2] Find the area of the shaded region bounded by $y=\frac{5}{3}, y=\pi, x=\frac{3\pi}{2}$, the y-axis and the x-axis.[3] Explain why the area of the shaded region is between $5$ units$^2$ and $\frac{3\pi2}{2}$ units$^2$.[1]

Accepted Answer

(i) $A=(1,-13)$, $r=5\sqrt{2}$ (ii) $(x-1)^2+(y+13)^2=50$ (iii) $(x+13)^2+(y-1)^2=50$

2025 SST PRELIMS P1 Q10

2025 SST PRELIMS P1 Q10

Solution:

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