| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing basic circle properties. Parts (i)-(iii) require only direct reading/simple substitution, while part (iv) involves standard tangent verification using perpendicular distance formula or substitution—all routine C1 techniques with no problem-solving insight needed. |
| 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 |
A circle has equation $(x - 5)^2 + (y - 2)^2 = 20$.
\begin{enumerate}[label=(\roman*)]
\item State the coordinates of the centre and the radius of this circle. [2]
\item State, with a reason, whether or not this circle intersects the $y$-axis. [2]
\item Find the equation of the line parallel to the line $y = 2x$ that passes through the centre of the circle. [2]
\item Show that the line $y = 2x + 2$ is a tangent to the circle. State the coordinates of the point of contact. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2009 Q13 [11]}}