lf the axes are rotated through an angle $180^{o}$ the equation $2 x - 3 y + 4 = 0$ becomes

2 X - 3 Y - 4 = 0

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2 X + 3 Y - 4 = 0

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3 X - 2 Y + 4 = 0

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3 X + 2 Y + 4 = 0

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Solution

The correct option is A $2 X - 3 Y - 4 = 0$
Given equation is $2 x - 3 y + 4 = 0$
We know that
$x = X cos θ - Y sin θ$
$y = X sin θ + Y cos θ$
Here $θ = 180^{0}$
$\Rightarrow x = - X, y = - Y$
So, the transformed equation is
$- 2 X + 3 Y + 4 = 0$
or, $2 X - 3 Y - 4 = 0$

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