2023 NYJC P1 Q8
The curve $C$ is a circle with equation ${{x}^{2}}+{{y}^{2}}-8x-6y-20=0$.
(a)
$C$ crosses the positive $x$-axis at point $A$. Find the equation of ${{l}_{1}}$, the tangent to the circle at point $A$.
[4]
(b)
$C$ crosses the positive $y$-axis at point $B$. Find the gradient of ${{l}_{2}}$, the tangent to the circle at point $B$. Hence, find the acute angle between the ${{l}_{1}}$ and ${{l}_{2}}$.
[4]
(c)
The minor segment bounded by $C$ and the y-axis is defined as $R$. Find the volume generated when $R$ is rotated four right angles about the $y$-axis, leaving your answer to $1$ decimal place.
[3]
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