Moderate -0.8 This is a straightforward C1 circles question requiring standard techniques: finding circle equation from diameter endpoints (midpoint for centre, distance formula for radius), finding x-intercepts by substituting y=0, and using perpendicular gradient for tangent. All steps are routine applications of formulas with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature and 11 marks total.
The point \(A\) has coordinates \((4, 6)\).
Given that \(OA\), where \(O\) is the origin, is a diameter of circle \(C\),
find an equation for \(C\). [4]
Circle \(C\) crosses the \(x\)-axis at \(O\) and at the point \(B\).
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the coordinates of \(B\). [2]
\item Find an equation for the tangent to \(C\) at \(B\), giving your answer in the form \(ax + by = c\), where \(a\), \(b\) and \(c\) are integers. [5]
The point $A$ has coordinates $(4, 6)$.
Given that $OA$, where $O$ is the origin, is a diameter of circle $C$,
\begin{enumerate}[label=(\roman*)]
\item find an equation for $C$. [4]
\end{enumerate}
Circle $C$ crosses the $x$-axis at $O$ and at the point $B$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the coordinates of $B$. [2]
\item Find an equation for the tangent to $C$ at $B$, giving your answer in the form $ax + by = c$, where $a$, $b$ and $c$ are integers. [5]
</enumerate}
\hfill \mbox{\textit{OCR C1 Q7 [11]}}