Question:
The common tangent to the circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}+6 x+8 y-24=0$ also passes through the point:
Correct Option: , 3
Solution:
By the diagram, $d_{c_{1} c_{2}}=\left|r_{1}-r_{2}\right|$
Equation of common tangent is,
$\mathrm{S}_{1}-\mathrm{S}_{2}=0$
$6 x+8 y-20=0 \Rightarrow 3 x+4 y-10=0$
Hence $(6,-2)$ lies on it.
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