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Shift the origin to a suitable point so ...

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.

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