1. Tardigrade
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  4. The vertices of a Δ ABC lie on a rectangular hyperbola such that the orthocentre of the triangle is (.3,2.) and the asymptotes of the rectangular hyperbola are parallel to coordinate axes. If the two perpendicular tangents of the hyperbola intersect at (.1,1.), then equation of the rectangular hyperbola is

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Q. The vertices of a $\Delta ABC$ lie on a rectangular hyperbola such that the orthocentre of the triangle is $\left(\right.3,2\left.\right)$ and the asymptotes of the rectangular hyperbola are parallel to coordinate axes. If the two perpendicular tangents of the hyperbola intersect at $\left(\right.1,1\left.\right),$ then equation of the rectangular hyperbola is

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
Equation of asymptotes are $x-1=0$ and $y-1=0$ hyperbola passes through $\left(\right.3,2\left.\right)$
Equation of rectangular hyperbola is
$\left(x - 1\right)\left(y - 1\right)=0$
$\Rightarrow xy+1=x+y$