JEE Main · 2005 · 08 May 2005 · Offline · Straight Lines

The line parallel to the

x

-axis and passing through the intersection of the lines ax +

2 b y + 3 b = 0

and

b x - 2 a y - 3 a = 0

, where

(a, b) \neq = (0, 0)

Answer: (A)

Solution

Consider the family of lines

a x + 2 b y + 3 b + λ (b x - 2 a y - 3 a) = 0

passing through the intersection. For a line parallel to the

x

-axis the coefficient of

x

must vanish, so

a + λb = 0

, giving

λ = - \frac{a}{b}

. Substituting this value, the

x

-terms cancel and the relation becomes

\frac{2 ( a ^{2} + b ^{2} )}{b} y + \frac{3 ( a ^{2} + b ^{2} )}{b} = 0

, so

y = - \frac{3}{2}

. The line is horizontal and lies

\frac{3}{2}

units below the

x

-axis.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option