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(C) The given equations of the circles are:$C_1: x^2+y^2+4x-6y-3=0$$C_2: x^2+y^2+4x-2y+1=0$Comparing with the general equation $x^2+y^2+2gx+2fy+c=0$:F

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$1$

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(C) The given equations of the circles are:$C_1: x^2+y^2+4x-6y-3=0$$C_2: x^2+y^2+4x-2y+1=0$Comparing with the general equation $x^2+y^2+2gx+2fy+c=0$:For $C_1$: $g=2, f=-3, c=-3$. Centre $O_1 = (-2, 3)$,Radius $r_1 = \sqrt{g^2+f^2-c} = \sqrt{4+9+3} = \sqrt{16} = 4$.For $C_2$: $g=2, f=-1, c=1$. Centre $O_2 = (-2, 1)$,Radius $r_2 = \sqrt{g^2+f^2-c} = \sqrt{4+1-1} = \sqrt{4} = 2$.The distance between the centres $O_1O_2 = \sqrt{(-2 - (-2))^2 + (3-1)^2} = \sqrt{0^2 + 2^2} = 2$.We observe that $|r_1 - r_2| = |4 - 2| = 2$.Since the distance between the centres $O_1O_2 = |r_1 - r_2|$,the two circles touch each other internally.When two circles touch internally,there is exactly $1$ common tangent.

The number of possible common tangents that can be drawn to the circles $x^2+y^2+4x-6y-3=0$ and $x^2+y^2+4x-2y+1=0$ is

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