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(A) The bisectors of the angles between the co-ordinate axes are $y = x$ and $y = -x$,which can be written as $x - y = 0$ and $x + y = 0$.Since the re

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$x^2 - y^2 + 4x + 6y - 5 = 0$

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(A) The bisectors of the angles between the co-ordinate axes are $y = x$ and $y = -x$,which can be written as $x - y = 0$ and $x + y = 0$.Since the required lines are parallel to these bisectors and pass through $(-2, 3)$,their equations are:$1) (x - y) - (-2 - 3) = 0 \implies x - y + 5 = 0$$2) (x + y) - (-2 + 3) = 0 \implies x + y - 1 = 0$The joint equation is $(x - y + 5)(x + y - 1) = 0$.Expanding this: $x(x + y - 1) - y(x + y - 1) + 5(x + y - 1) = 0$$x^2 + xy - x - xy - y^2 + y + 5x + 5y - 5 = 0$$x^2 - y^2 + 4x + 6y - 5 = 0$.

The joint equation of two lines passing through $(-2, 3)$ and parallel to the bisectors of the angle between the co-ordinate axes is

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