If `bx+cy=a`, there `a, b, c` are of the same sign, be a line such that the area enclosed by the line and the axes of reference is `1/8` square units, then : (A) `b,a,c` are in G.P. (B) `b, 2a, c` arein G.P. (C) `b, a/2, c` are in A.P. (D) `b, -2a, c` are in G.P.

Options

A. `b, a, c` and `G.P.`
B. `b, 2a, -c` are in `G.P.`
C. `b, a//2, c` are in `A.P.`
D. `b, +2a, c` are in `G.P.`

Answer

D

Explanation

Given equation is `bx + cy = a`, where `a,b,c` are of the intersects the axes at
`A((a)/(b),0)` and `B(0,(a)/(c))`
`rArr` Area enclosed between the axes and the line
`= (1)/(2).(a)/(b).(a)/(c) = (a^(2))/(2bc) = (1)/(8)`
`4a^(2)=bc`, so `b +- 2a,c` are in `G.P`.