When the axes are rotated through an angle $90^{o}$ the equation $5 x - 2 y + 7 = 0$ transforms to

2 X - 5 Y + 7 = 0

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2 X + 5 Y - 7 = 0

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2 X - 5 Y - 7 = 0

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2 X + 5 Y + 7 = 0

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Solution

The correct option is B $2 X + 5 Y - 7 = 0$
Given equation is $5 x - 2 y + 7 = 0$
We know that,
$x = X cos θ - Y sin θ$
$y = X sin θ + Y cos θ$
Given $θ = 90^{0}$
$\Rightarrow x = - Y$ and $y = X$
So, the transformed equation is
$- 5 Y - 2 X + 7 = 0$
$\Rightarrow 2 X + 5 Y - 7 = 0$

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(1, 1)

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