A) \[2{{X}^{2}}+{{Y}^{2}}=6\]
B) \[2{{X}^{2}}+{{Y}^{2}}+6=0\]
C) \[{{X}^{2}}+2{{Y}^{2}}=6\]
D) \[2{{X}^{2}}+{{Y}^{2}}=0\]
Correct Answer: A
Solution :
We have the equation\[2{{x}^{2}}+{{y}^{2}}-4x+4y=0\] ...(i) Since, axes are to be shifted to the point\[(1,-2)\] therefore substitute\[x=X+1\]and\[y=Y-2\]in Eq. (i), we get \[2{{(X+1\text{ })}^{2}}+{{(Y-2)}^{2}}-4(X+1)+4(Y-2)=0\] \[\Rightarrow \]\[2({{X}^{2}}+1+2X)+{{y}^{2}}+4-4Y-4X\]\[-4+4Y-8=0\] \[\Rightarrow \] \[2{{X}^{2}}+{{Y}^{2}}-6=0\] \[\Rightarrow \] \[2{{X}^{2}}+{{Y}^{2}}=6\] which is the required equation.
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