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Q.
The number of common tangents that can be drawn to the circle $x^{2}+y^{2}-4 x-6 y-3=0$ and $x^{2}+y^{2}+2 x+2 y+1=0$ is
Conic Sections
Solution:
The two circles are $x^{2}+y^{2}-4 x-6 y-3=0$ and $x^{2}+y^{2}+2 x+2 y+1=0$
Center : $C _{1} \equiv(2,3), C _{2} \equiv(-1,-1)$ radii : $r _{1}=4, r _{2}=1$
We have $C_{1} C_{2}=5=r_{1}+r_{2}$, therefore there are 3 common tangents to the given circles.