Question

The equation of the conic with focus at $(1,-1)$ directrix along $x-y+1=0$ and with eccentricity $\sqrt{2}$ is.

• A. $x^2-y^2=1$
• B. $xy=1$
• C. $2xy-4x+4y+1=0$
• D. $2xy+4x-4y-1=0$

Answer 1

The correct option is C $2xy-4x+4y+1=0$

Let P(x, y) be any point on conic. Then,
$\sqrt{(x-1{)}^2+(y+1{)}^2}=\sqrt{2}\left(\frac{x-y+1}{\sqrt{2}}\right)$
$\Rightarrow (x-1{)}^2+(y+1{)}^2=(x-y+1{)}^2$
$\Rightarrow 2xy-4x-4y+1=0$ is the required equation of conic.