Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  MayJun  (P19709/13)  Q#7
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Question
The point P(x,y) is moving along the curve in such a way that the rate of change of y is constant. Find the values of x at the points at which the rate of change of x is equal to half the rate of change of y.
Solution
We are required to find values of x at the points for which;
Let , then;
Rate of change of with respect to is;
Therefore;
We are given that;
Therefore;
Rule for differentiation of is:
Rule for differentiation of is:
Hence;
We recognize that it is a quadratic equation.
Standard form of quadratic equation is;
The solution of this quadratic equation is;
Therefore, for the given equation;
Now we have two options.










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