Exam-Style Question on Circle Equations

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 270. This question is similar to one that appeared on 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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If you need more practice try the self-checking interactive exercises called Circle Equations.

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