SPS SPS SM 2022 October — Question 9 7 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2022
SessionOctober
Marks7
TopicCircles
TypeDistance from centre to line
DifficultyStandard +0.3 This is a slightly above-average question requiring students to find the circle's radius, then verify perpendicularity between the radius and line (or show distance from centre to line equals radius). It involves multiple standard techniques (distance formula, gradient calculations, perpendicularity condition) but follows a well-established problem type with clear steps and no novel insight required.
Spec1.03b Straight lines: parallel and perpendicular relationships1.03d 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. The centre of a circle C is the point (-1, 3) and C passes through the point (1, -1). The straight line L passes through the points (1, 9) and (4, 3). Show that L is a tangent to C. [7]

In this question you must show detailed reasoning.

The centre of a circle C is the point (-1, 3) and C passes through the point (1, -1).
The straight line L passes through the points (1, 9) and (4, 3).
Show that L is a tangent to C. [7]

\hfill \mbox{\textit{SPS SPS SM 2022 Q9 [7]}}