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If the origin is shifted to the point `(1,-2)` without the rotation of the axes, what do the following equations become? (i) `2x^2+y^2-4x+4y=0` (ii) `y^2-4x+4y+8=0`

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(i) Substituting `x=X+1` and `y=Y+(-2)=Y-2` in the equation `2x^2+y^2=4x+4y=0`, we get
`2(X+1)^2+(Y-2)^2-4(X+1)+4(Y-2)=0`
or `2X^2+Y^2=6`
(ii) Substituting `x=X=1` and `y-Y-2` in the equation `y^2-4x+4y+8=0`, we get
`(Y-2)^2-4(X+1)+4(Y-2)+8-0`
or `Y^2=4X`
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