If $x + 2 = 0$ and $y = 1$ are the equation of asymptotes of rectangular hyperbola passing through (1,0).Then which of the following is(are) not the equation(s) of hyperbola :

x y + 2 y - 1 = 0

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x y - 2 y + 1 = 0

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x y - 2 y - 1 = 0

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x y - x + 2 y + 1 = 0

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Solution

The correct options are
A $x y + 2 y - 1 = 0$
B $x y - 2 y + 1 = 0$
C $x y - 2 y - 1 = 0$
Equation of hyperbola is of the form $(x + 2) (y - 1) = k$
Since, it passes through $(1, 0)$
Therefore, $(1 + 2) (0 - 1) = k$
$\Rightarrow k = - 3$
Therefore, equation of hyperbola is $x y - x + 2 y + 1 = 0$

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