IGCSE/GCSE/O & A Level/IB/University Student Forum
Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: HUSH1994 on December 16, 2010, 03:05:30 pm
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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
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2 minutes.
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Whether you like or not differentiation is necessary to solve part (b).
The tangent to the curve is parallel to the y+3x=9 right ? So the gradient of the tangent will be 3 as well.
Differentiating the curve equation gives : 2x - 4
We must now find the point on the curve at which dy/dx = 3
Hence, 2x-4 = 3
x = 3.5
Corresponding y coordinate is : -1.5
Therefore, the coordinates of Q are : (3.5,-1.5)