Let the point P α , β be at a unit distance from each of the two lines L 1 : 3 x - 4 y + 12 = 0 , and L 2 : 8 x + 6 y + 11 = 0 . If P lies below L 1 and above L 2 , then 100 α + β is equal to

Step-by-step solution

Given, the point P α , β be at a unit distance from each of the two lines L 1 : 3 x - 4 y + 12 = 0 , and L 2 : 8 x + 6 y + 11 = 0 , so on plotting the diagram we get, ​​​​​​​ Now, L 1 : 3 x - 4 y + 12 = 0 and L 2 : 8 x + 6 y + 11 = 0 Since L 1 & L 2 are perpendicular so it will form square of unit length, so equation of angle bisector of L 1 and L 2 of angle containing origin and will pass through α , β , so Equation of angle bisector will be, 3 x - 4 y + 12 3 2 + 4 2 = 8 x + 6 y + 11 8 2 + 6