If the line l 1 : 3 y - 2 x = 3 is the angular bisector of the lines l 2 : x - y + 1 = 0 and l 3 : α x + β y + 17 = 0 , then α 2 + β 2 - α - β is equal to ............

Step-by-step solution

Given, L 1 : 3 y - 2 x = 3 is angular bisector of L 2 : x - y + 1 = 0 and L 3 : α x + β y + 17 = 0 Now finding point of intersection of L 1   &   L 2 we get, 0 ,   1 And point will lie on L 3 , so α × 0 + β × 1 + 17 = 0 ⇒ β = - 17 Any point, say - 3 2 , 0 on L 1 should be equidistant from lines L 2   &   L 3 Now using the formula of distance of a point from the line we get, ⇒ - 3 2 - 0 + 1 1 2 + 1 2 = - 3 α 2 + 0 + 17 α 2 + (