this is a question from a past paper,im not sure which year but it is pure one,i need a way by co-ordinate geometry equations to solve it,not differentiation.
Q.The equation of the curve is y=x^2-4x+7 and the equation of the line is y+3x=9. The curve and the line intersect at the points A and B.
(i)the mid-point of AB is M,show that the co-ordinates of M are (0.5,7.5) [not the problem,its easy
]
(ii) Find the coordinates of the point Q on the curve at which the tangent is parallel to the line y+3x=9. [this is the real pain]
thanks,please help as soon as possible,as i have an exam on saturday