The conic for the equation displaystyle{left({x}+{2}right)}^{2}+{left({y}-{1}right)}^{2}={4} and also describe the translation of the conic from the standard position.

The conic for the equation ${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}=4$ and also describe the translation of the conic from the standard position.
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Raheem Donnelly
Consider the equation,
${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}=4$
The above equation is also written as follows,
${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}={2}^{2}$
Now compare the above equation with the standard form of the equation of the circle, that is ${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}.$
So,
$h=-2,k=1\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}r=2$
Thus, the equation ${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}=4$ is the equation of circle with center at (-2, 1)
and radius $r=2$ as shown below,
Therefore, the graph has been shifted 1 unit upward and 2 units to the left from the standard position.