Challenging Questions

Mathematics – Compulsory Part

Learning Unit: Equations of circles

Question M0-13-02

Let \(C\) be the circle \(x^2 + y^2 – 2x + 6y + 1 = 0\) and \(L\) be the line \(x + y = 4\).

1. Show that \(L\) does not meet \(C\).
2. Find the coordinates of the nearest and furthest points on \(C\) from \(L\).
3. Hence, find the tangents of \(C\) that are parallel to \(L\).

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