Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#7

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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.


We are required to find values of x at the points for which;

Let , then;

Rate of change of  with respect to  is;


We are given that;


Rule for differentiation of  is:

Rule for differentiation of  is:


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.