 # Conic for the equation (x+1)^2=4(-1)(y^(-2)) and also describe the translation of the from standard position. usagirl007A 2020-11-12 Answered

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

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Consider the equation,
${\left(x+1\right)}^{2}=4\left(-1\right)\left(y-2\right)$
Now, compare the above equation with the standard equation of the parabola, that is, ${\left(x-h\right)}^{2}=4p\left(y-k\right).$
$h=-1,k=2\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}p=-1$
Thus, the equation ${\left(x+1\right)}^{2}=4\left(-1\right)\left(y-2\right)$
is the equation of the parabola with vertex at $\left(-1,2\right)$
and the directed distance from vertex to focus lies at $\left(h,k+p\right)=\left(-1,2-1\right)=\left(-1,1\right)$ and the directrix is,
$y=k-p$
$=2-\left(-1\right)$
$=3$
The graph is shown below,
Therefore, the graph has been shifted 2 units upward and 1 unit to the left from the standard position.