SPS SPS SM Pure 2021 May — Question 6 7 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionMay
Marks7
TopicCircles
TypeTangent equation involving finding the point of tangency
DifficultyChallenging +1.2 This is a solid coordinate geometry problem requiring multiple techniques: finding perpendicular lines to tangents, solving simultaneous equations for the center, then calculating the radius. While it involves several steps and careful geometric reasoning about tangent properties, the individual techniques are all standard A-level material with no novel insights required. The 7-mark allocation confirms it's substantial but not exceptional difficulty.
Spec1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle

In this question you must show detailed reasoning. A circle touches the lines \(y = \frac{1}{2}x\) and \(y = 2x\) at \((6, 3)\) and \((3, 6)\) respectively. \includegraphics{figure_6} Find the equation of the circle. [7]

In this question you must show detailed reasoning.

A circle touches the lines $y = \frac{1}{2}x$ and $y = 2x$ at $(6, 3)$ and $(3, 6)$ respectively.

\includegraphics{figure_6}

Find the equation of the circle. [7]

\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q6 [7]}}