| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Moderate -0.3 Part (a) is routine completion of the square to find centre and radius (standard C4 skill). Part (b) requires implicit differentiation to find dy/dx, which is a standard technique. Part (c) applies the gradient formula at a specific point to write the tangent equation. All parts are textbook exercises with no novel insight required, making this slightly easier than average for A-level. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.07s Parametric and implicit differentiation |
The circle $C$ has equation $x^2 + y^2 - 8x - 16y - 209 = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the centre of $C$ and the radius of $C$. [3]
\end{enumerate}
The point $P(x, y)$ lies on $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find, in terms of $x$ and $y$, the gradient of the tangent to $C$ at $P$. [3]
\item Hence or otherwise, find an equation of the tangent to $C$ at the point $(21, 8)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q19 [8]}}