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Question

lf the axes are translated to the point $$(-2, -3)$$ , then the equation $$\mathrm{x}^{2}+3\mathrm{y}^{2}+4\mathrm{x}+18\mathrm{y}+30=0$$ transforms to


A
X2+Y2=4
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B
X2+3Y2=1
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C
X2Y2=4
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D
X23Y2=1
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Solution

The correct option is B $$\mathrm{X}^{2}+3\mathrm{Y}^{2}=1$$
When the point $$(x,y)$$ changes to $$(X,Y)$$ on shifting the origin to $$(h,k)$$
Then, $$x=X+h,y=Y+k$$
$$x=X-2 , y=Y-3$$
So, the equation transform to 
$$(X-2)^2+3(Y-3)^2+4(X-2)+18(Y-3)+30=0$$
$$\Rightarrow X^2+3Y^2-1=0$$
So, the transformed eqn is $$X^2+3Y^2-1=0$$

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