Let a , b , c and d be non-zero numbers. If the point of intersection of the lines 4 a x + 2 a y + c = 0 & 5 b x + 2 b y + d = 0 lies in the fourth quadrant and is equidistant from the two axes then

Step-by-step solution

Let ( h , k ) be the intersection of the two given lines its equidistant from both axes. ∴   h = k Since it lies in the fourth quadrant, the point can be written as ( h , - h ) , where h > 0 . ( h , - h ) lies on both the lines. ∴   4 a h - 2 a h + c =0 ∴  c = - 2 a h ∴   h = - c 2 a 5 b h - 2 b h + d =0 ∴  d = - 3 b h ∴   h = - d 3 b ∴   - c 2 a = - d 3 b ∴   3 b c - 2 a d =0