Question

The equation of second degree $x^2+2\sqrt{2}xy+2y^2+4x+4\sqrt{2}y+1=0$ represents a pair of straight lines. The distance between them is

• A. $4$
• B. $\frac{4}{\sqrt{3}}$
• C. $2$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

The correct option is C $2$

Distance between pair of straight lines defined by $a{x}^2+2hxy+b{y}^2+2gxy+2fy+c=0$ is:

2$\sqrt{\frac{g^2-ac}{a(a+b)}}$ or 2$\sqrt{\frac{f^2-bc}{b(a+b)}}$

By, using any one of the two formulae distance can be calculated. In current given equation,

$g=2;a=1;c=1;b=2$

$\therefore$ using $\sqrt{\frac{g^2-ac}{a(a+b)}}$,

Distance = $2units$