Question

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

Answer 1

Let coordinate of the intersection point in fourth quadrant be `(alpha,-alpha)`.
Since, `(alpha,-alpha)` lies on both lines `4ax+2ay+c=0` and `5bx+2by+d=0`
`:. 4aa-2aa+c=0impliesalpha=(-c)/(2a)`……….`(i)`
and `5balpha-2balpha+d=0impliesalpha=(-d)/(3b)`.........`(ii)`
From Eqs. `(i)` and `(ii)`, we get
`(-c)/(2a)=(-d)/(3b)implies3bc=2ad`
`implies2ad-3bc=0`