(d) find the area of the quadrilateral SPQPʹ. (3) 8. The rectangular hyperbola has equation = where is a positive constant. H xy c2, c The point , 0 is a general point on t H. ≠ An equation for the tangent to at is given by H P The points and lie on A B H. The tangent to at and the tangent to at meet at the point . H A H B Find, in terms of the coordinates of and the coordinates of c, A B. (5) 9. (a) Prove by induction that, for , (5) (b) A sequence of numbers is defined by = 0, = 32, u1 u2 = 6un+1 8un 1 un+2 n – ≥ Prove by induction that, for , = 4n+1 2n+3 un – (7) TOTAL FOR PAPER: 75 MARKS END Paper Reference(s) 6667/01 Edexcel GCE
(d) find the area of the quadrilateral SPQPʹ. (3) 8. The rectangular hyperbola H has equation xy = c2, where c is a positive constant. The point , t ≠ 0 is a general point on H. An equation for the tangent to H at P is given by The points A and B lie on H. The tangent to H at A and the tangent to H at B meet at the point . Find, in terms of c, the coordinates of A and the coordinates of B. (5) 9. (a) Prove by induction that, for , (5) (b) A sequence of numbers is defined by u1 = 0, u2 = 32, un+2 = 6un+1 – 8un n ≥ 1 Prove by induction that, for , un = 4n+1 – 2n+3 (7) TOTAL FOR PAPER: 75 MARKS END Paper Reference(s) 6667/01 Edexcel GCE
fp1_all-past-papers.docx