iiiiiiiimmmmmmmmmppppppp 3-; x^2 +2 root.2xy +2y^2 +4x +4 root2y +1=0 ; the dist. between thease lin

Gaurav Mishra

iiiiiiiimmmmmmmmmppppppp 3-; x^2 +2 root.2xy +2y^2 +4x +4 root2y +1=0 ; the dist. between thease lines

Deepak Aggarwal

Given equation is x² + 2(2)^1/2 xy + 2y² + 4x + 4(2)^1/2 y + 1 = 0

Comparing it with general equation of second degree i.e.

ax² + 2hxy + by² + 2gx + 2fy + c = 0

we have a = 1, h = (2)^1/2, b = 2, g = 2, f = 2(2)^1/2 and c = 1.

It this equation represents pair of two straight parallel lines then,

h²- ab = 0

So, (2) - (1)(2) = 0

So, the given lines represent straight parallel lines.

Now, the distance between them(d) is given by

d = 2 ((g² - ac) / a(a + b))^1/2 = 2 ((4 - 1)/(1)(1 + 2))^1/2 = 2(1) = 2 units (Ans).........