The asymptotes of the hyperbola x y-3 x-2 y=0 are-

Question

The asymptotes of the hyperbola x y-3 x-2 y=0 are- (A) x -2=0 and y -3=0 (B) x -3=0 and y -2=0 (C) x +2=0 and y +3=0 (D) x+3=0 and y+2=0

Tardigrade Admin · Accepted Answer

Let equation of asymptotes be xy -3 x -2 y +λ=0. Then a b c+2 f g h-a f2-b g2-c h2=0 ⇒ (3/2)-(λ/4)=0 ⇒ λ=6 ∴ Equation of asymptotes is x y-3 x-2 y+6=0 i.e., (x-2)(y-3)=0.

Q. The asymptotes of the hyperbola $x y - 3 x - 2 y = 0$ are-

$x - 2 = 0$ and $y - 3 = 0$

$x - 3 = 0$ and $y - 2 = 0$

$x + 2 = 0$ and $y + 3 = 0$

$x + 3 = 0$ and $y + 2 = 0$

Let equation of asymptotes be $x y - 3 x - 2 y + λ = 0$ .
Then $ab c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$
$\Rightarrow \frac{3}{2} - \frac{λ}{4} = 0$
$\Rightarrow λ = 6$
$∴$ Equation of asymptotes is $x y - 3 x - 2 y + 6 = 0$
i.e., $(x - 2) (y - 3) = 0$ .

Q. The asymptotes of the hyperbola xy−3x−2y=0 are-

x−2=0 and y−3=0

x−3=0 and y−2=0

x+2=0 and y+3=0

x+3=0 and y+2=0