| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent from external point - find equation |
| Difficulty | Standard +0.8 Part (a) is routine expansion of circle equation (2 marks). Part (b)(i) requires finding tangent equations from an external point, involving simultaneous equations with a discriminant condition or perpendicular distance formula—this is non-trivial problem-solving worth 6 marks. Part (b)(ii) adds further calculation to find contact points. The 12-mark total and multi-step reasoning with tangents from external points elevates this above average difficulty, but it remains a standard circle geometry question without requiring exceptional insight. |
| 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 equations |
| Answer | Marks |
|---|---|
| 18 | 12 |
| Total | 120 |
| Answer | Marks |
|---|---|
| number | Additional page, if required. |
| Answer | Marks |
|---|---|
| number | Additional page, if required. |
Question 18:
18 | 12
Total | 120
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.\begin{enumerate}[label=(\alph*)]
\item A circle C has centre $(-3, -1)$ and radius $\sqrt{5}$. Show that the equation of C can be written as $x^2 + y^2 + 6x + 2y + 5 = 0$. [2]
\item \begin{enumerate}[label=(\roman*)]
\item Find the equations of the tangents to C that pass through the origin O. [6]
\item Determine the coordinates of the points where the tangents touch the circle. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2024 Q18 [12]}}