Shift the origin to a suitable point so that the equation `y^2+4y+8x-2=0` will not contain a term in `y` and the constant term.

Options

A. `((3)/(4),-2)`
B. `(-(3)/(4),2)`
C. `(2,-(3)/(4))`
D. `(-2,(3)/(4))`

Explanation

Let the origin be shifted tiom (h,k). Then `x=X+h and y=Y+k`. Substituting `x=X+h,y=Y+k` in the equation `y^(2)+4y+8x-2=0`
`(Y+k^(2))+4(Y+k)+8(x+h)-2=0`
`rArr Y^(2)+(4+2k)Y+8X+(k^(2)+4k+8h)=0`
For this equation to be free from the term containing Y and the cosntant term, we must have
`4+2k=0 and k^(2)+4k+8h-2=0`
`rArr k=-2 and h=(3)/(4)`
Hence, the origin must be shifted at the point (3/4,-2)