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

X^{2} + Y^{2} = 4

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X^{2} + 3 Y^{2} = 1

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X^{2} - Y^{2} = 4

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X^{2} - 3 Y^{2} = 1

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Solution

The correct option is B $X^{2} + 3 Y^{2} = 1$
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
$(X - 2)^{2} + 3 (Y - 3)^{2} + 4 (X - 2) + 18 (Y - 3) + 30 = 0$
$\Rightarrow X^{2} + 3 Y^{2} - 1 = 0$
So, the transformed eqn is $X^{2} + 3 Y^{2} - 1 = 0$

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lf the axes are translated to the point (−2,−3) , then the equation x2+3y2+4x+18y+30=0 transforms to

The correct option is B X2+3Y2=1When the point (x,y) changes to (X,Y) on shifting the origin to (h,k)Then, x=X+h,y=Y+kx=X−2,y=Y−3So, the equation transform to (X−2)2+3(Y−3)2+4(X−2)+18(Y−3)+30=0⇒X2+3Y2−1=0So, the transformed eqn is X2+3Y2−1=0

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