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If the axes are transformed to the point (− 1,1), then the equation
$3 x^2+y^2+2 x+4 y+15=0$ would transform
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$3 x^2+y^2+2 x+4 y+15=0$ would transform
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Verified Answer
The correct answer is:
$3 x^2+y^2-4 x+6 y+21=0$
When the point (x, y) changes to (X, Y) on shifting the origin to (h, k)
Then,
$\begin{aligned} & X=x+h \text { and } Y=y+k \\ \Rightarrow & X=x-1 \text { and } Y=y+1\end{aligned}$
So, the equation transform to,
$\begin{aligned} & 3(x-1)^2+(y+1)^2+2(x-1)+4(y+1)+15=0 \\ & 3\left(x^2+1-2 x\right)+y^2+1+2 y+2 x-2+ \\ & \Rightarrow 3 x^2+y^2-4 x+6 y+21=0\end{aligned}$
Then,
$\begin{aligned} & X=x+h \text { and } Y=y+k \\ \Rightarrow & X=x-1 \text { and } Y=y+1\end{aligned}$
So, the equation transform to,
$\begin{aligned} & 3(x-1)^2+(y+1)^2+2(x-1)+4(y+1)+15=0 \\ & 3\left(x^2+1-2 x\right)+y^2+1+2 y+2 x-2+ \\ & \Rightarrow 3 x^2+y^2-4 x+6 y+21=0\end{aligned}$
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