Given that, $x^{2} + y^{2} + 4 x - 2 y = - 1$
The equation of a circle in the $x y$ -plane is shown above. What is the radius of the circle?

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Solution

The correct option is C $2$
Given, $x^{2} + y^{2} + 4 x - 2 y = - 1$
$\Rightarrow x^{2} + 4 x + y^{2} - 2 y = - 1$
$\Rightarrow (x^{2} + 4 x + 4) + (y^{2} - 2 y + 1) = - 1 + 4 + 1$
$\Rightarrow (x + 2)^{2} + (y - 1)^{2} = 2^{2}$
Clearly, $= (- 2, 1)$
Radius $= 2$
Hence, option A is correct.

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