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

1

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2

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3

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none of these

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Solution

The correct option is A $1$
Given point $(- 1, 2)$

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

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 $Distance from center - Radius$

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 $2 - 1 = 1$

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