A circle has equation
$$x ^ { 2 } + y ^ { 2 } - 10 x - 6 = 0$$
Find the centre and the radius of the circle.
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An equilateral triangle has one vertex at the origin, and one side along the line \(x = 8\), as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{9cd7f38d-a2a1-4fd3-9ed9-cb389e8ee3b6-14_697_750_1311_735}
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Show that the vertex at the origin lies inside the circle \(x ^ { 2 } + y ^ { 2 } - 10 x - 6 = 0\)
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(ii) Prove that the triangle lies completely within the circle \(x ^ { 2 } + y ^ { 2 } - 10 x - 6 = 0\)