| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Moderate -0.8 This is a straightforward C1 circles question testing standard techniques: expanding circle equation from centre-radius form (routine algebra), finding y-intercepts by substituting x=0 (basic substitution), and finding a tangent equation using perpendicular gradients (standard procedure). All parts are textbook exercises requiring only direct application of learned methods with no problem-solving or insight needed. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.03f Circle properties: angles, chords, tangents |
\includegraphics{figure_10}
Fig. 10 shows a circle with centre C$(2, 1)$ and radius 5.
\begin{enumerate}[label=(\roman*)]
\item Show that the equation of the circle may be written as
$$x^2 + y^2 - 4x - 2y - 20 = 0.$$ [3]
\item Find the coordinates of the points P and Q where the circle cuts the $y$-axis. Leave your answers in the form $a \pm \sqrt{b}$. [3]
\item Verify that the point A$(5, -3)$ lies on the circle.
Show that the tangent to the circle at A has equation $4y = 3x - 27$. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q10 [12]}}