| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Standard +0.3 Part (a) requires completing the square to find the condition for a real circle (radius² > 0), a standard technique. Part (b) involves implicit differentiation to find dy/dx = 1/2, then solving simultaneous equations. Both parts are routine applications of circle geometry and differentiation with no novel insight required, making this slightly easier than average. |
| Spec | 1.03d 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 equations1.07s Parametric and implicit differentiation |
A circle $C$ has equation $x^2 + y^2 - 6x + 10y + k = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find the set of possible values of $k$. [2]
\item It is given that $k = -46$.
Determine the coordinates of the two points on $C$ at which the gradient of the tangent is $\frac{1}{2}$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2023 Q4 [7]}}