The curve $C_1$ has equation $y = \frac{x^2 - 8x + 28}{2 - x}$. The curve $C_2$ has equation \

Question

The curve $C_1$ has equation $y = \frac{x^2 - 8x + 28}{2 - x}$. The curve $C_2$ has equation $\frac{(x-6)^2}{16} + \frac{y^2}{25} = 1$. Sketch $C_1$ and $C_2$ on the same diagram, stating the coordinates of any vertices, turning points, intersections with the $x$-axis and the equations of any asymptotes.[7] Find the volume of solid obtained when the smaller region bounded by $C_1$ and $C_2$ is rotated through $2\pi$ radians about the $x$-axis.[4]

Accepted Answer

(a) $C_1$: turning points $(-2,12)$, $(6,-4)$, asymptotes $x=2$, $y=-x+6$, no $x$-intercepts; $C_2$: vertices $(2,0)$, $(10,0)$, $(6,5)$, $(6,-5)$ (b) $58.7\text{ units}^3$

2025 EJC P2 Q3

2025 EJC P2 Q3

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