Question

A hyperbola has focus at origin , its eccentricity is $\sqrt{2}$ & corresponding directrix is $x+y+1=0$. The equation of its asymptotes is/are:

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

Answer 1

Answer: (A), (C)

$x+1=0$
$y+1=0$

Here, we can see that

$P{F}^2=e^{2}P{S}^2{x}^2+y^2=2.[\frac{x+y+1}{\sqrt{2}}{]}^2$

Solving it we get, $2x+2y+2xy+1=0$

Let $C=2x+2y+2xy+1$

$\frac{dC}{dx}=2+2y=0\Rightarrow y+1=0\frac{dC}{dy}=2+2x=0\Rightarrow x+1=0$