page 07 MARKS 12. Circle C1 has equation ( ) ( ) x y − + + = 2 2 13 4 100. Circle C2 has equation x y x y c + + − + = 2 2 14 22 0 . P C2 C1 (a) (i) Write down the coordinates of the centre of C1. (ii) The centre of C1 lies on the circumference of C2. Show that c = −455. The line joining the centres of the circles intersects C1 at P. (b) (i) Determine the ratio in which P divides the line joining the centres of the circles. (ii) Hence, or otherwise, determine the coordinates of P. P is the centre of a third circle, C3. C2 touches C3 internally. (c) Determine the equation of C3. [END OF QUESTION PAPER] 1 1 2 2 1 page 08 [BLANK PAGE] DO NOT WRITE ON THIS PAGE Write your answers clearly in the spaces provided in this booklet. The size of the space provided for an answer should not be taken as an indication of how much to write. It is not necessary to use all the space. Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are attempting. Use blue or black ink. Before leaving the examination room you must give this booklet to the Invigilator; if you do not, you may lose all the marks for this paper. FOR OFFICIAL USE X747/76/02 Mathematics Paper 2 Answer Booklet Fill in these boxes and read what is printed below. Full name of centre Town Forename(s) Surname Number of seat Day Month Year Scottish candidate number © Mark Date of birth H National Qualications 2018 THURSDAY, 3 MAY 10:30 AM – 12:00 NOON A/PB page 02 [BLANK PAGE] DO NOT WRITE ON THIS PAGE page 03 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 1. page 04 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 2.(a) 2.(b) page 05 3. DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 4. page 06 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 5.(a) 5.(b) 5.(c) page 07 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 6.(a) (i) 6.(b) 6.(a) (ii) page 08 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 7.(a) (i) 7.(a) (ii) 7.(b) page 09 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 7.(c) (i) 7.(c) (ii) page 10 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 8.(a) 8.(b) (i) 8.(b) (ii) page 11 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 9. page 12 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 10. page 13 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 11.(a) 11.(b) page 14 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 12.(a) (i) 12.(b) (i) 12.(a) (ii) page 15 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 12.(b) (ii) 12.(c) page 16 DO NOT WRITE IN THIS MARGIN ENTER NUMBER OF QUESTION ADDITIONAL SPACE FOR ANSWERS page 17 DO NOT WRITE IN THIS MARGIN ENTER NUMBER OF QUESTION ADDITIONAL SPACE FOR ANSWERS page 18 DO NOT WRITE IN THIS MARGIN ENTER NUMBER OF QUESTION ADDITIONAL SPACE FOR ANSWERS page 19 DO NOT WRITE IN THIS MARGIN ENTER NUMBER OF QUESTION ADDITIONAL SPACE FOR ANSWERS page 20 For Marker’s Use Question No Marks/Grades