(B) Let the new coordinates be $(x', y')$. The transformation equations are $x = x' + 2$ and $y = y' + 3$.Substituting these into the given equation $

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(B) Let the new coordinates be $(x', y')$. The transformation equations are $x = x' + 2$ and $y = y' + 3$.Substituting these into the given equation $x^{2} + y^{2} - 4x - 6y + 9 = 0$:$(x' + 2)^{2} + (y' + 3)^{2} - 4(x' + 2) - 6(y' + 3) + 9 = 0$Expanding the terms:$(x'^{2} + 4x' + 4) + (y'^{2} + 6y' + 9) - 4x' - 8 - 6y' - 18 + 9 = 0$Combining like terms:$x'^{2} + y'^{2} + (4x' - 4x') + (6y' - 6y') + (4 + 9 - 8 - 18 + 9) = 0$$x'^{2} + y'^{2} - 4 = 0$Therefore, the new equation is $x^{2} + y^{2} = 4$.

Class 11 Mathematics Rectangular Cartesian Co-ordinates Transformation of axes

Medium

Without changing the direction of the axes, the origin is shifted to the point $(2, 3)$. Then the equation $x^{2} + y^{2} - 4x - 6y + 9 = 0$ changes to

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A
$x^{2} + y^{2} + 4 = 0$
B
$x^{2} + y^{2} = 4$
C
$x^{2} + y^{2} - 8x - 12y + 48 = 0$
D
$x^{2} + y^{2} = 9$

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Rectangular Cartesian Co-ordinates

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Transformation of axes

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Without changing the direction of the axes, the origin is shifted to the point $(2, 3)$. Then the equation $x^{2} + y^{2} - 4x - 6y + 9 = 0$ changes to

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