Question

The line x+y+1 = 0 is an asymptote of x² - y² + x - y - 2 = 0. The other asymptote is

• A. x+y=0
• B. x-y=0
• C. x-y=1
• D. x-y+1=0

Answer 1

Answer: (B)

x-y=0

Answer 2

Since coefficient of x² + coefficient of y² = 0.

The given hyperbola is rectangular hyperbola.

∴ The asymptotes are perpendicular.

Let the other asymptote e x – y = λ. It passes through the centre of the given Hyperbola $\left( \frac { - 1 } { 2 } , - \frac { 1 } { 2 } \right)$

∴ λ = 0.

∴ The required equation of asymptote is x- y = 0.