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Question id: 270. This question is similar to one that appeared in a GCSE Higher paper in 2017. The use of a calculator is allowed.

(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis.

The equation of circle \(A\) is \(x^2+y^2=25\). This circle is translated by the vector \( \begin{pmatrix} 0 \\ 4 \\ \end{pmatrix} \) to give circle \(B\).

(b) Draw a sketch of circle \(B\) clearly labelling the points of intersection with the y-axis.

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