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

Question

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 (A) xy=2x+y-2 (B) 2xy=x+2y+5 (C) xy+1=x+y (D) none of these

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<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-u1xrrakbcwmzf50u.jpg" /> Equation of asymptotes are x-1=0 and y-1=0 hyperbola passes through (.3,2.) Equation of rectangular hyperbola is (x - 1)(y - 1)=0 ⇒ xy+1=x+y

$x y = 2 x + y - 2$

$2 x y = x + 2 y + 5$

$x y + 1 = x + y$

none of these

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

xy=2x+y−2

2xy=x+2y+5

xy+1=x+y

none of these

Equation of asymptotes are x−1=0 and y−1=0 hyperbola passes through (3,2) Equation of rectangular hyperbola is (x−1)(y−1)=0 ⇒xy+1=x+y

$x y = 2 x + y - 2$

$2 x y = x + 2 y + 5$

$x y + 1 = x + y$

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