# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#2

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**Question**

A curve is such that . Given that the curve passes through the point , find the

equation of the curve.

**Solution**

We are given that curve passes through the point and we are required to find the equation of the curve.

We can find equation of the curve from its derivative through integration;

For the given case;

Therefore;

Rule for integration of is:

If a point lies on the curve , we can find out value of . We substitute values of and in the equation obtained from integration of the derivative of the curve i.e. .

We are given a point on the curve . Substituting these values of x & y coordinates of the point we can find .

Hence we can write the equation of the curve as follows;

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