| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2019 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.3 This is a straightforward coordinate geometry question testing standard circle and line intersection techniques. Part (a) is trivial midpoint calculation, part (b) requires expanding circle equation (routine), part (c) involves substituting a line into circle equation and solving a quadratic (standard procedure), and part (d) uses basic area formula. All steps are textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
The points $A(-2, 4)$ and $B(6, 10)$ are such that $AB$ is the diameter of a circle.
\begin{enumerate}[label=(\alph*)]
\item Show that the centre of the circle has coordinates $(2, 7)$. [1]
\item The equation of the circle is $x^2 + y^2 + ax + by + c = 0$.
Determine the values of $a$, $b$, $c$. [3]
\end{enumerate}
A straight line, with equation $y = x + 6$, passes through the point $A$ and cuts the circle again at the point $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Find the coordinates of $C$. [5]
\item Calculate the exact area of the triangle $ABC$. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2019 Q09 [12]}}