Question 8 - A-Level Maths

A circle $C$ has centre $( 3,4 )$ and radius $3 \sqrt { } 2$. A straight line $l$ has equation $y = x + 3$.
1. Write down an equation of the circle $C$.
2. Calculate the exact coordinates of the two points where the line $l$ intersects $C$, giving your answers in surds.
3. Find the distance between these two points.
\begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{c85316fe-5c59-4cb3-8cb8-d95a4e97af70-5_730_983_278_404}
\end{figure} The curve $C$, shown in Fig. 2, represents the graph of $$y = \frac { x ^ { 2 } } { 25 } , x \geq 0 .$$ The points $A$ and $B$ on the curve $C$ have $x$-coordinates 5 and 10 respectively.
Write down the $y$-coordinates of $A$ and $B$.
Find an equation of the tangent to $C$ at $A$. The finite region $R$ is enclosed by $C$, the $y$-axis and the lines through $A$ and $B$ parallel to the $x$-axis.
For points $( x , y )$ on $C$, express $x$ in terms of $y$.
Use integration to find the area of $R$. END