Let a, b, c and d be non-zero numbers. If the point of intersection...

Let $( h, k )$ be the intersection of the two given lines its equidistant from both axes.

$∴ \left|h\right| = \left|k\right|$

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.

$∴ 4ah - 2ah + c =0$

$∴ c = - 2ah$ $∴ h = \dfrac{- c}{2a}$

$5bh - 2bh + d =0$

$∴ d = - 3bh$ $∴ h = \dfrac{- d}{3b}$

$∴ \dfrac{- c}{2a} = \dfrac{- d}{3b}$

$∴ 3bc - 2ad =0$