Standard +0.3 This is a standard locus problem requiring algebraic manipulation to convert the given condition into circle form. Students substitute z = x + iy, expand |z - 6i|² = 4|z - 3|², and complete the square. While it involves several algebraic steps, the technique is routine and commonly practiced in Further Maths complex numbers topics, making it slightly easier than average.
The point \(P\) represents a complex number \(z\) on an Argand diagram such that
$$|z - 6i| = 2|z - 3|.$$
Show that, as \(z\) varies, the locus of \(P\) is a circle, stating the radius and the coordinates of the centre of this circle.
[6 marks]
The point $P$ represents a complex number $z$ on an Argand diagram such that
$$|z - 6i| = 2|z - 3|.$$
Show that, as $z$ varies, the locus of $P$ is a circle, stating the radius and the coordinates of the centre of this circle.
[6 marks]
\hfill \mbox{\textit{SPS SPS FM 2021 Q3 [6]}}