# Str Lines

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

1
Ram lakhan Meena ·

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.....................

21
eragon24 _Retired ·

hey jus check in the q if its a,c,b are in gp......

1357
Manish Shankar ·

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 y2=4x with slope as (-1/r)

So i m getting none of these

11
Gone.. ·

Ans given is (c)

11
Gone.. ·

o ya sorry...its a,c,b in Gp..q edited.

21
eragon24 _Retired ·

C).forms a triangle whose area is constant

a ,c, b in gp so c2=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

=c22ab=1/2

hence area constant