The curve $y=\dfrac{25}{(x+2)^2}-1$ meets the positive $x$-axis at $A$. The shaded region \(P\

Question

The curve $y=\dfrac{25}{(x+2)^2}-1$ meets the positive $x$-axis at $A$. The shaded region $P$ is bounded by the curve and the coordinate axes. The shaded region $Q$ is bounded by the curve, the $x$-axis and the line $x=8$. (i) Find the coordinates of $A$. (ii) Find the areas of $P$ and $Q$. (iii) Find the ratio of the area of $P$ to the area of $Q$.

Accepted Answer

(i) $A=(3,0)$ (ii) $P=\dfrac92\text{ units}^2$, $Q=\dfrac52\text{ units}^2$ (iii) $9:5$

Rational curve with positive and negative regions

Rational curve with positive and negative regions

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