A rectangular hyperbola passing through (3,2) | vedclass

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(D) The asymptotes of a rectangular hyperbola are parallel to the coordinate axes,so its equation is of the form $(x - h)(y - k) = c$. Since the point

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$xy = x + y + 1$

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(D) The asymptotes of a rectangular hyperbola are parallel to the coordinate axes,so its equation is of the form $(x - h)(y - k) = c$. Since the point of intersection of the two perpendicular tangents is the center of the hyperbola,we have $(h, k) = (1, 1)$. Thus,the equation is $(x - 1)(y - 1) = c$. Since the hyperbola passes through $(3, 2)$,we substitute these coordinates: $(3 - 1)(2 - 1) = c$ $\Rightarrow 2 	imes 1 = c$ $\Rightarrow c = 2$. Substituting $c = 2$ into the equation,we get $(x - 1)(y - 1) = 2$. Expanding this,we get $xy - x - y + 1 = 2$,which simplifies to $xy = x + y + 1$.

$A$ rectangular hyperbola passing through $(3,2)$ has its asymptotes parallel to the coordinate axes. If $(1,1)$ is the point of intersection of the two perpendicular tangents of that hyperbola,then its equation is

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