Mathematics - Circle Question with Solution | TestHub

Given circles are $x^2+y^2-8x-2y+1=0$ and $x^2+y^2+6x+8y=0$ Their centres and radius are $$C_1(4,1),r_1=\sqrt{16}=4$$ $$C_2(-3,-4),r_2=\sqrt{25}=5$$ Now, $C_1{C}_2=\sqrt{49+25}=\sqrt{74}$ $$r_1-r_2=-1,r_1+r_2=9$$ Since, $r_1-r_2<C_1{C}_2<r_1+r_2$ $\therefore$ Number of common tangents $=2$