Determine the number of points of intersection of the circle \( x^{2}+y^{2}+6 x-4 y+8=0 \) with ...

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Determine the number of points of intersection of the circle \( x^{2}+y^{2}+6 x-4 y+8=0 \) with each of the following lines:
\[
4 x+3 y-12=0
\]
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