Created by T Madas Question 273 (*****) A curve C and a straight line L have respective equations C : y = 4x x − 25 x 16 and L : x + y = 18 a) Show that L is a tangent to C , at some point to be found b) Verify the answer of part (a) by an alternative method c) Show further that L does not meet C again SPX-G , proof Created by T Madas Created by T Madas Question 274 (*****) The distinct points A , B and C lie on the curve with equation xy = p , where p is a positive constant Given that ABC is a right angle, show that the tangent to the curve at B , is perpendicular to AC SP-C , proof Created by T Madas Created by T Madas Question 275 (*****) A quadratic curve has equation ( ) f ( x ) ≡ x + x + 20 + k x − x − 12 , where k is a constant Given that the point P ( −2, p ) is the minimum point of the curve, determine the value of each of the constants p and k MP1-T , p = 80 , k = 7 Created by T Madas