The equation of a circle is $$\(x^{2}+y^{2}+p x+2 y+q=0\)$$, where $$\(p\)$$ and $$\(q\)$$ are constants. Express the equation in the form $$\((x-a)^{2}+(y-b)^{2}=r^{2}\)$$, where $$\(a\)$$ is to be given in terms of $$\(p\)$$ and $$\(r^{2}\)$$ is to be given in terms of $$\(p\)$$ and $$\(q\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . The line with equation $$\(x+2 y=10\)$$ is the tangent to the circle at the point $$\(A(4,3)\)$$.

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