| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Normal to circle at point |
| Difficulty | Moderate -0.3 This is a standard C2 circle question requiring completion of the square to find centre and radius, solving a quadratic for x-intercepts, and using perpendicular gradient property for the tangent. All techniques are routine for this level, though part (d) requires recognizing that radius AT is perpendicular to the tangent, making it slightly more than pure recall. |
| Spec | 1.03b 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 |
The circle $C$, with centre at the point $A$, has equation $x^2 + y^2 - 10x + 9 = 0$.
Find
\begin{enumerate}[label=(\alph*)]
\item the coordinates of $A$,
[2]
\item the radius of $C$,
[2]
\item the coordinates of the points at which $C$ crosses the $x$-axis.
[2]
\end{enumerate}
Given that the line $l$ with gradient $\frac{7}{T}$ is a tangent to $C$, and that $l$ touches $C$ at the point $T$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find an equation of the line which passes through $A$ and $T$.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q8 [9]}}