The shortest distance from the point $M(-1,2)$ to the circle $x^2+y^2-2x-4y+4=0$ is

The correct option is A $1$

Given point $(-1,2)$

Given circle is $x^2+y^2-2x-4y+4=0$

Center of circle is $(-g,-f)=(1,2)$

Radius of circle is $\sqrt{g^2+f^2-c}$

$\Rightarrow \sqrt{1+4-4}=1$

The shortest distance is given by $\text{Distance from center}-\text{Radius}$

Distance from center $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\Rightarrow \sqrt{(1+1{)}^2+(2-2{)}^2}=2$

So the shortest distance is $2-1=1$