| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.8 This is a straightforward multi-part coordinate geometry question requiring standard techniques: midpoint formula, gradient calculations, perpendicular lines, and simultaneous equations. All parts follow routine procedures with no novel problem-solving required, making it easier than average but not trivial due to the arithmetic involved across multiple parts. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.07m Tangents and normals: gradient and equations |
16.
\section*{Figure 3}
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\includegraphics[max width=\textwidth, alt={}]{90893903-4f36-4974-8eaa-0f462f35f442-08_581_575_395_609}
\end{center}
The points $A ( - 3 , - 2 )$ and $B ( 8,4 )$ are at the ends of a diameter of the circle shown in Fig. 3.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the centre of the circle.
\item Find an equation of the diameter $A B$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.
\item Find an equation of tangent to the circle at $B$.
The line $l$ passes through $A$ and the origin.
\item Find the coordinates of the point at which $l$ intersects the tangent to the circle at $B$, giving your answer as exact fractions.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q16 [13]}}