The equation of the diameter of the circle \( 3\left(x^{2}+y^{2}\right)-2 x+6 y-9=0 \) which is ...

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The equation of the diameter of the circle \( 3\left(x^{2}+y^{2}\right)-2 x+6 y-9=0 \) which is perpendicular to the line \( 2 x+3 y=12 \) is
(a) \( 3 x-2 y=3 \)
(b) \( 3 x-2 y+1=0 \)
(c) \( 3 x-2 y=0 \)
(d) none of these
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