The equations of the asymptotes of the hyperbola xy +3x - 2y -10= 0 are

Question

The equations of the asymptotes of the hyperbola xy +3x - 2y -10= 0 are (A) x =- 2, y = -3 (B) x = 2, y = - 3 (C) x =2, y = 3 (D) x =4, y = 3

Tardigrade Admin · Accepted Answer

We have equation of hyperbola is x y+3 x-2 y-10=0 x y+3 x-2 y-6=4 (x-2)(y+3)=4 We know that asymptote of hyperbola x y=c is x=0 and y=0. ∴ Asymptote of hyperbola (x-2)(y+3)=4 is x-2=0, y+3=0 ⇒ x=2, y=-3

Q. The equations of the asymptotes of the hyperbola $x y + 3 x - 2 y - 10 = 0$ are

$x = - 2, y = - 3$

$x = 2, y = - 3$

$x = 2, y = 3$

$x = 4, y = 3$

$x = 3, y = 4$

We have equation of hyperbola is
$x y + 3 x - 2 y - 10 = 0$
$x y + 3 x - 2 y - 6 = 4$
$(x - 2) (y + 3) = 4$
We know that asymptote of hyperbola
$x y = c$ is $x = 0$ and $y = 0$ .
$∴$ Asymptote of hyperbola
$(x - 2) (y + 3) = 4$ is $x - 2 = 0, y + 3 = 0$
$\Rightarrow x = 2, y = - 3$

Q. The equations of the asymptotes of the hyperbola xy+3x−2y−10=0 are

x=−2,y=−3

x=2,y=−3

x=2,y=3

x=4,y=3

x=3,y=4

We have equation of hyperbola is xy+3x−2y−10=0 xy+3x−2y−6=4 (x−2)(y+3)=4 We know that asymptote of hyperbola xy=c is x=0 and y=0. ∴ Asymptote of hyperbola (x−2)(y+3)=4 is x−2=0,y+3=0 ⇒x=2,y=−3