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 and 5 b x+2 b y+ d =0 lies in the fourth quadrant and is equidistant from the two coordinate axes, then

Step-by-step solution

Given: 4 ax +2 ay + c =05 b x+2 b y+d=0 Eqn. (i) b- (ii) a -a b x+b c-a d=0 x = bc - ad ab Putting the value of x in eqn. (ii), we get aligned & 5 b ( b c-a d a b )+2 b y+d=0 & y= 4 a d-5 b c 2 a b aligned Point of intersection is P ( b c-a d a b , 4 a d-5 b c 2 a b ) P is in fourth quadrant and equidistant from the two coordinate axes. aligned & - 4 a d-5 b c 2 a b = b c-a d a b & -4 a d+5 b c=2 b c-2 a d & 3 b c=2 a b 3 b c-2 a d=0 aligned