The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) `(1/2 ,3/4)` (b) `(1,3)` (c) `(3,1)` (d) `(3/4 ,1/2)`

Options

A. `(3//4,1//2)`
B. `(1//2,3//4)`
C. `(-3//4,-1//2)`
D. none of these

Answer

A

Explanation

We have,
`ax + by + c = 0`
where `3a +2b + 4c=0`
`rArr ax + by -(1)/(4)(3a + 2b) = 0 rArr a(x-(3)/(4)) + by (y -(1)/(2)) = 0`
Clearly, it repesents a family of line passing thorugh the intersection of the line.
`x - (3)/(4) = 0` and `y -(1)/(2) = 0` i.e.,the point `(3//4,1//2)`
ALITER We have , `3a + 2b + 4c= 0`
`rArr (3)/(4)a+ (b)/(2)+ c = 0 rArr (3//4,1//2)` lies on `ax + by + c=0`