Mathematics - Circle Question with Solution | TestHub

Let, $x^2+y^2=16$ or $x^2+y^2=4^2$ radius of circle $r_1=4$, centre ${\mathrm{C}}_1(0,0)$ we have, $x^2+y^2-2y=0$ $$\begin{array}{rl}\Rightarrow & x^2+\left(y^2-2y+1\right)-1=0\text{ or }{x}^2+(y-1{)}^2\\ =& 1^2\end{array}$$ Radius 1, centre ${\mathrm{C}}_2(0,1)$ $$\begin{array}{rl}& \left|C_1{C}_2\right|=1\\ & \left|r_2-r_1\right|=|4-1|=3\\ & \left|C_1{C}_2\right|<\left|r_2-r_1\right|\end{array}$$ no common tangents for these two circles.