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

Options

A. 2bc-3ad=0
B. 2bc+3ad=0
C. 2ad - 3bc =0
D. 3bc + 2ad =0

Answer

C

Explanation

Let coordinates of the intersection point in fourth quadrant be `(prop , -prop) " Since " (prop , -prop)` lies on both lines 4ax+2ay +c=0 and 5bx +2by +d=0
`4a prop -2aprop + c =0 Rightarrow prop = (-c)/(2a)`
` and 5bprop -2bprop +d =0 Rightarrow prop= (-d)/(3b)`
From Eqs. (i) and (ii)
` (-c)/(2a) = (-d)/(3b)`
`Rightarrow 3bc =2ab`
2ab-3bc = 0