Mathematics - Circle Question with Solution | TestHub

Given$x^2+y^2-4x-6y-12=0$

$C_1\left(2, 3\right), r_1=\sqrt{2^2+3^2+12}=\sqrt{25}=5$

And$x^2+y^2+6x+18y+26=0$

$C_2\left(-3,-9\right), r_2=\sqrt{3^2+9^2-26}$

$=\sqrt{90-26}=8$

Then,$C_1{C}_2=\sqrt{5^2+12^2}=13$

$C_1{C}_2=r_1+r_2$

$\Rightarrow$Externally touching circles.

$\Rightarrow 3$common tangents.