Created by T Madas Question 259 (****+) A quadratic curve C passes through the points P ( a, b ) and Q ( 2a, 2b ) , where a and b are constants The gradient at any given point on C is given by dy = 2x − dx Find an equation for C , in terms of a C1Y , y = x − x + 2a Created by T Madas Created by T Madas Question 260 (****+) A curve has equation y = x3 + k − 19 , x x>0, where k is a positive constant If the y coordinate of the stationary point of this curve is 45 , find the value of k SYN-Q , k = 96 Created by T Madas Created by T Madas Question 261 (****+) y y= x2 + x4 O k x 2k The figure above shows the graph of the curve with equation y= x2 + x4 , x>0 The area of the region between the curve and the x axis for k ≤ x ≤ 2k , where k is a positive constant, is exactly a) Show clearly that 9k − 2k − = b) Hence find the value of k , showing further that there is no other value of k which satisfies the equation of part (b) C2V , k = Created by T Madas