Created by T Madas Question 152 (***+) The point P ( 3, k ) lies on the curve with equation y = x + ax − , where a and k are constants Given that the gradient at P is determine the value of a and the value of k SYN-G , a = −3, k = −4 Created by T Madas Created by T Madas Question 153 (***+) The curve C has equation y = x3 − x + x − a) Find an equation of the normal to C at the point P ( 3,5 ) The point Q lies on C so that the normal to the curve at Q is parallel to the normal to the curve at P b) Find an equation of the normal to the curve at Q x + y = 48 , x + 27 y + 176 = Created by T Madas Created by T Madas Question 154 (***+) The point P (1,0 ) lies on the curve C with equation y = x3 − x , x ∈ » a) Find an equation of the tangent to C at P , giving the answer in the form y = mx + c , where m and c are constants The tangent to C at P meets C again at the point Q b) Find the coordinates of Q y = x − , Q ( −2, −6 ) Created by T Madas