| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Topic | Circles |
| Type | Circle touching axes |
| Difficulty | Moderate -0.8 Part (a) requires recognizing that a circle touching the x-axis has radius equal to the absolute value of the y-coordinate of its center, then writing the standard circle equation—straightforward recall. Part (b) involves setting up a horizontal line y=k, substituting into the circle equation, and using the chord length formula or symmetry to find k, which is a standard textbook exercise requiring only routine algebraic manipulation with no novel insight. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
\includegraphics{figure_4}
A circle with centre $(9, -6)$ touches the $x$-axis as shown in Figure 4.
(a) Write down an equation for the circle. [3]
A line $l$ is parallel to the $x$-axis.
The line $l$ cuts the circle at points $P$ and $Q$.
Given that the distance $PQ$ is 8
(b) find the two possible equations for $l$. [4]
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q8 [7]}}