| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Standard +0.3 This is a straightforward multi-part circle question requiring midpoint formula, equation of a line, perpendicular gradient for tangent, and simultaneous equations. All techniques are standard C1 procedures with no novel insight needed, making it slightly easier than average but still requiring careful execution 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 circle |
\includegraphics{figure_3}
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. [2]
\item Find an equation of the diameter $AB$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [4]
\item Find an equation of tangent to the circle at $B$. [3]
\end{enumerate}
The line $l$ passes through $A$ and the origin.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the coordinates of the point at which $l$ intersects the tangent to the circle at $B$, giving your answer as exact fractions. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q16 [13]}}