York
2021-02-11
Answered

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

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Raheem Donnelly

Answered 2021-02-12
Author has **75** answers

Consider the equation,

${(x+2)}^{2}+{(y-1)}^{2}=4$

The above equation is also written as follows,

$(x+2)}^{2}+{(y-1)}^{2}={2}^{2$

Now compare the above equation with the standard form of the equation of the circle, that is${(x-h)}^{2}+{(y-k)}^{2}={r}^{2}.$

So,

$h=-2,k=1{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}r=2$

Thus, the equation${(x+2)}^{2}+{(y-1)}^{2}=4$ 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.

The above equation is also written as follows,

Now compare the above equation with the standard form of the equation of the circle, that is

So,

Thus, the equation

and radius

Therefore, the graph has been shifted 1 unit upward and 2 units to the left from the standard position.

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