Edexcel C2 2013 June — Question 10 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2013
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircles
TypeTangent from external point - find equation
DifficultyStandard +0.3 This is a straightforward C2 circle question requiring basic geometric understanding. Part (a) is trivial (writing down the circle equation given center and radius). Part (b) uses the standard right-angle property of tangents with Pythagoras' theorem - a routine application requiring no novel insight, making it slightly easier than average.
Spec1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.03f Circle properties: angles, chords, tangents

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-16_723_979_207_495} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} The circle \(C\) has radius 5 and touches the \(y\)-axis at the point \(( 0,9 )\), as shown in Figure 4.
  1. Write down an equation for the circle \(C\), that is shown in Figure 4. A line through the point \(P ( 8 , - 7 )\) is a tangent to the circle \(C\) at the point \(T\).
  2. Find the length of \(P T\).

10.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-16_723_979_207_495}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

The circle $C$ has radius 5 and touches the $y$-axis at the point $( 0,9 )$, as shown in Figure 4.
\begin{enumerate}[label=(\alph*)]
\item Write down an equation for the circle $C$, that is shown in Figure 4.

A line through the point $P ( 8 , - 7 )$ is a tangent to the circle $C$ at the point $T$.
\item Find the length of $P T$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2 2013 Q10 [6]}}