| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Range of parameter for intersection |
| Difficulty | Moderate -0.8 Part (a) is routine completion of the square to find centre and radius from general circle equation—standard bookwork. Part (b) requires substituting the line equation into the circle, forming a quadratic in x, and using the discriminant condition, which is a standard technique taught explicitly for line-circle intersection problems. The question is straightforward with clear structure and no novel insight required, making it easier than average but not trivial due to the algebraic manipulation needed in part (b). |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x) |
A circle with centre $C$ has equation $x^2 + y^2 - 6x + 4y + 4 = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the coordinates of $C$, [2]
\item the radius of the circle. [1]
\end{enumerate}
\item Determine the set of values of $k$ for which the line $y = kx - 3$ does not intersect or touch the circle. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2019 Q2 [8]}}