page 09 MARKS 15. A circle has centre C(8,12). The point P(5,13) lies on the circle as shown. O T C(8,12) P(5,13) y x (a) Find the equation of the tangent at P. The tangent from P meets the y-axis at the point T. (b) (i) State the coordinates of T. (ii) Find the equation of the circle that passes through the points C, P and T. [END OF QUESTION PAPER] 3 1 3 page 10 [BLANK PAGE] DO NOT WRITE ON THIS PAGE page 11 [BLANK PAGE] DO NOT WRITE ON THIS PAGE page 12 [BLANK PAGE] DO NOT WRITE ON THIS PAGE Write your answers clearly in the spaces provided in the answer booklet. The size of the space provided for an answer is not an indication of how much to write. You do not need to use all the space. Additional space for answers is provided at the end of the answer 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 your answer booklet to the Invigilator; if you do not, you may lose all the marks for this paper. FOR OFFICIAL USE X847/76/02 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 National Qualications 2019 THURSDAY, 2 MAY 11:00 AM – 12:45 PM A/PB H page 02 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 1.(a) 1.(b) 1.(c) page 03 2. DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 3.(a) 3.(b) page 04 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 4.(a) 4.(b) (i) 4.(b) (ii) 5. An additional diagram, if required, can be found on page 16. y x –2 –3 –4 –5 –6 –7 –8 –1 4 5 6 7 8 3 2 1 O page 05 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 6.(a) 6.(b) page 06 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 7.(a) 7.(b) page 07 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 8.(a) 8.(b) page 08 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 9.(a) 9.(b) page 09 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 10.(a) 10.(b) page 10 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 11.(a) page 11 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 11.(b) page 12 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 12. page 13 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 13. 14. page 14 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 15.(a) 15.(b) (i) page 15 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 15.(b) (ii) page 16 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER Additional diagram for question 5. y x –2 –3 –4 –5 –6 –7 –8 –1 4 5 6 7 8 3 2 1 O 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