Q. The equation $x^{2} + 2\sqrt{2}xy + 2y^{2} + 4x + 4\sqrt{2}\ y + 1 = 0$ represents a pair of lines which are parallel to each other. The distance between them is
A) 4 units
B) $2\sqrt{3}\$units
C) $4\sqrt{3}\$units
D) 2 units
Explanation
(d)
Here, $h = \sqrt{2},\ \ \ g = 2,\ \ a = 1,\ c = 1,\ \ b = 2,\ \ f = 2\sqrt{2}$
$\therefore Distance = 2\sqrt{\frac{g^{2} - ac}{a(a + b)}} = 2\sqrt{\frac{4 - 1}{1(1 + 2)}} = 2\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.