area is constant .....
since x intercept is -c/a and y intercept is -c/b.
so its area 1/2 (-c/b)(-c/a)
= 1/2(c^2/ab) and c^2=ab as the are in gp
=1/2 A CONSTANT AREA.....................
If a,c,b are in G.P then the line ax+by+c=0
(A) has a fixed direction
(B) always passes through a fixed point
(C) forms a triangle whose area is constant
(D) none of these
area is constant .....
since x intercept is -c/a and y intercept is -c/b.
so its area 1/2 (-c/b)(-c/a)
= 1/2(c^2/ab) and c^2=ab as the are in gp
=1/2 A CONSTANT AREA.....................
b/a=c/b=r
it becomes
y=-(a/b)x-c/b
y=-x/r-r
which is the equation of tangent to parabola y^{2}=4x with slope as (-1/r)
So i m getting none of these
C).forms a triangle whose area is constant
a ,c, b in gp so c^{2}=ab
this line ax +by +c=0 forms a right angled triangle at origin
points of intersection of this line with x and y axis respectively are (-c/a,0) and (0,-c/b)
area of this right angled triangle at origin is 12x-cax-cb
=c^{2}2ab=1/2
hence area constant