# The common tangent to the circle $x^{2}+y^{2}=4\:\:and\:\:x^{2}+y^{2}+6x+8y-24=0$  also passes through the point : Option 1) $(4,-2)$ Option 2) $(-6,4)$ Option 3) $(6,-2)$ Option 4) $(-4,6)$

P Plabita

$x^{2}+y^{2}-4=0$

$\\x^{2}+y^{2}+6x+8y-24=0$

common tangent will  be  $s_{1}-s_{2}=0$

$\\6x+8y=20\\\\\:3x+4y=10\\\\\:hence \:\:point \:(6,-2)\:\:lies\:\:on\:\:above \:\:line.$

Option 1)

$(4,-2)$

Option 2)

$(-6,4)$

Option 3)

$(6,-2)$

Option 4)

$(-4,6)$

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