OCR C1 2010 January — Question 8 9 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2010
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting general conic
DifficultyModerate -0.3 Part (i) is routine completing the square to find centre and radius. Part (ii) requires substituting the line equation into the circle equation and solving the resulting quadratic—a standard technique for C1. The arithmetic is straightforward with integer solutions, making this slightly easier than average but still requiring multiple steps and algebraic manipulation.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle

8 A circle has equation \(x ^ { 2 } + y ^ { 2 } + 6 x - 4 y - 4 = 0\).
  1. Find the centre and radius of the circle.
  2. Find the coordinates of the points where the circle meets the line with equation \(y = 3 x + 4\).

8 A circle has equation $x ^ { 2 } + y ^ { 2 } + 6 x - 4 y - 4 = 0$.\\
(i) Find the centre and radius of the circle.\\
(ii) Find the coordinates of the points where the circle meets the line with equation $y = 3 x + 4$.

\hfill \mbox{\textit{OCR C1 2010 Q8 [9]}}