A curve $C$ has parametric equations $$x = 2t + 3, y = 5 - 4t^2,$$ for all real values of $t$. T

Question

A curve $C$ has parametric equations $$x = 2t + 3, y = 5 - 4t^2,$$ for all real values of $t$. The line $N$ is the normal to $C$ at the point where $t = -\frac{1}{2}$. Find the cartesian equation of $N$.[3] Find the cartesian equation of $C$.[2] The region $R$ is bounded by $C$, $N$ and the $y$-axis. Without using a calculator, find the exact volume of the solid generated when the region $R$ is rotated through $2\pi$ radians about the $y$-axis.[5]

Accepted Answer

(a) $y=-\frac12x+5$. (b) $y=5-(x-3)^2$. (c) $\frac{28\pi}{3}$ cubic units.

2025 TMJC P1 Q8

2025 TMJC P1 Q8

Solution:

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