(2) 8. The rectangular hyperbola has equation = where is a positive constant. H xy c2, c The point 0, is a general point on P, t H. ≠ (a) Show that an equation for the tangent to at is H P + 2 = 2ct. x t y (4) The tangent to at the point meets the at the point and the at the point H P x-axis A y-axis B. Given that the area of the triangle where is the origin, is 36, OAB, O (b) find the exact value of expressing your answer in the form where is an integer. c, k√2, k (4) 9. M = . (a) Find det M. (1) The transformation represented by M maps the point 7, 1), where is a constant, S(2a a a – – onto the point (25, S –14). (b) Find the value of a. (3) The point has coordinates (6, 0). R Given that is the origin, O (c) find the area of triangle ORS. (2) Triangle is mapped onto triangle by the transformation represented by M. ORS OR 'S ' (d) Find the area of triangle OR 'S '. (2) Given that = A (e) describe fully the single geometrical transformation represented by A. (2)
(2) 8. The rectangular hyperbola H has equation xy = c2, where c is a positive constant. The point P, t ≠ 0, is a general point on H. (a) Show that an equation for the tangent to H at P is x + t 2 y = 2ct. (4) The tangent to H at the point P meets the x-axis at the point A and the y-axis at the point B. Given that the area of the triangle OAB, where O is the origin, is 36, (b) find the exact value of c, expressing your answer in the form k√2, where k is an integer. (4) 9. M = . (a) Find det M. (1) The transformation represented by M maps the point S(2a – 7, a – 1), where a is a constant, onto the point S (25, –14). (b) Find the value of a. (3) The point R has coordinates (6, 0). Given that O is the origin, (c) find the area of triangle ORS. (2) Triangle ORS is mapped onto triangle OR 'S ' by the transformation represented by M. (d) Find the area of triangle OR 'S '. (2) Given that A = (e) describe fully the single geometrical transformation represented by A. (2)