Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2017  MayJun  (P19709/13)  Q#3
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Question
Find the coordinates of the points of intersection of the curve with the curve .
Solution
If two lines (or a line and a curve) intersect each other at a point then that point lies on both lines i.e. coordinates of that point have same values on both lines (or on the line and the curve). Therefore, we can equate coordinates of both lines i.e. equate equations of both the lines (or the line and the curve).
Equation of the curve 1 is;
Equation of the curve 2 is;
Equating both equations;
Let then . Therefore;
Now we have two options.




Since 







Two values of x indicate that there are two intersection points.
With xcoordinate of point of intersection of two lines (or line and the curve) at hand, we can find the ycoordinate of the point of intersection of two lines (or line and the curve) by substituting value of xcoordinate of the point of intersection in any of the two equations;
We choose;











Hence, coordinates of the points of intersection of the two curves are;


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