If the orthocenter of the triangle formed by the lines 2 x + 3 y - 1 = 0 , x + 2 y + 1 = 0 and a x + b y - 1 = 0 lies at origin, then 1 a + 1 b =

Step-by-step solution

We have triangle ∆ A B C A B :   2 x + 3 y - 1 = 0     . . . 1 Slope m 1 = - 2 3 B C :   x + 2 y + 1 = 0     . . . 2 Slope m 2 = - 1 2 C A :   a x + b y - 1 = 0     . . . 3 Slope m 3 = - a b We know, the orthocenter of a triangle is the point of intersection of altitudes passing through the vertices of the triangle. Here we have altitudes A D ,   B E   and   C F So, the family of line passing through the vertex B , is, 2 x + 3 y - 1 + λ x + 2 y