Find the centre and the radius of the circle \( x^{2}+y^{2}-4 x+2 y-4=0 \). Hence, or otherwise,...

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Find the centre and the radius of the circle \( x^{2}+y^{2}-4 x+2 y-4=0 \).
Hence, or otherwise, prove that \( x+1=0 \) is a tangent to the circle. Calculate the coordinates of the point of contact. If this point of contact is \( \mathrm{A} \), find the coordinates of the other end of the diameter through A.
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