The equation of a rectangular hyperbola whose asymptotes are x=3 and y=5 and passing through (7,8) is

Question

The equation of a rectangular hyperbola whose asymptotes are x=3 and y=5 and passing through (7,8) is (A) x y-3 y+5 x+3=0 (B) x y+3 y+4 x+3=0 (C) x y-3 y+5 x-3=0 (D) x y-3 y-5 x+3=0

Tardigrade Admin · Accepted Answer

The equation of the rectangular hyperbola is (x-3)(y-5)+λ=0 It passes through (7,8). Hence, 4 × 3+λ or λ=-12 ∴ x y-5 x-3 y+15-12=0 or x y-3 y-5 x+3=0

Q. The equation of a rectangular hyperbola whose asymptotes are $x = 3$ and $y = 5$ and passing through $(7, 8)$ is

$x y - 3 y + 5 x + 3 = 0$

$x y + 3 y + 4 x + 3 = 0$

$x y - 3 y + 5 x - 3 = 0$

$x y - 3 y - 5 x + 3 = 0$

The equation of the rectangular hyperbola is
$(x - 3) (y - 5) + λ = 0$
It passes through $(7, 8)$ . Hence,
$4 \times 3 + λ$ or $λ = - 12$
$∴ x y - 5 x - 3 y + 15 - 12 = 0$
or $x y - 3 y - 5 x + 3 = 0$

Q. The equation of a rectangular hyperbola whose asymptotes are x=3 and y=5 and passing through (7,8) is

xy−3y+5x+3=0

xy+3y+4x+3=0

xy−3y+5x−3=0

xy−3y−5x+3=0