Question

The equation of the line passing through the centre of a rectangular hyperbola is x - y -1=0. If one of its asymptote is

3x - 4y -6=0. The equation of the other asymptote is

• A. $4x - 3y + 8 = 0$
• B. $4x + 3y + 17 = 0$
• C. $3x - 2y + 15 = 0$
• D. None of these

Answer 1

Answer: (B)

$4x + 3y + 17 = 0$

Answer 2

Since asymptotes of rectangular hyperbola are perpendicular to each other.

$\because$ Given asymptote is $3x - 4y - 6 = 0$

$\therefore$ Other asymptotes is $4x + 3y + \lambda = 0$……………….(1)

Given centre of hyperbola lies on x - y -1=0 since asymptotes pass through the centre of hyperbola

$\therefore$ Centre is the point of intersection of $x - y - 1 = 0$and $3x - 4y - 6 = 0$

$\therefore$ Centre is $( - 2, - 3)$ also $( - 2, - 3)$ lies on (1) then - 8 - 9 +λ = 0

$\therefore$ λ = 17

Hence other asymptote is $4x + 3y + 17 = 0$

[ from (1)]