Question 9 - A-Level Maths

Express the equation of the circle in the form $$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$ where $a , b$ and $k$ are constants to be found.
9
State the coordinates of $P$ 9
Find the $y$-coordinate of $Q$
\section*{Question 9 continues on the next page} 9
The line segment $Q R$ is a tangent to the circle as shown in Figure 2 below. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{deec0d32-b031-4227-bc80-7150a0acbc94-18_885_1180_456_495}
\end{figure} The point $R$ has coordinates $( 9 , - 3 )$.
Find the angle QPR
Give your answer in radians to three significant figures.
It is given that $$f ( x ) = 5 x ^ { 3 } + x$$ Use differentiation from first principles to prove that $$f ^ { \prime } ( x ) = 15 x ^ { 2 } + 1$$