IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

snippy

Anyone who can answer this qn!!!! plz help me out, StRaIgHt LiNeS

if a,c,b are in G.P, then the area of the triangle formed by ax + by + c =0 with the coordinate axes is
a.a^2 b b.1/2 c.2a+b d.25

rooney

See x intercept is -c/a and y intercept is -c/b.
So, area of triangle is c²/2ab
Let b=ar , c = ar²So,area = r³/2 ........ r=common ratio

Its not matching with either option,

nadeemoidu

a,c,b are in GP => c² = ab

the intercepts are -c/a and -b/a

area of the triangle is c²/2ab = 1/2

answer (B)

rooney

ohh sorry...i thought it was a,b,c in G.P. lol

VINCE_7N

if a c b are in GP then
c²=ab (1)
intercept on the 2 coordinate axis is y= -c/a x=-c/b
area of the triangle =1/2c^2 /ab=1/2
answer b

akshay.khare91

since the equation of line is ax+by+c=0

then the x intercept= -c/a (putting y=0)
also y intercept= -c/b (putting x=0)

and it is forming a right angle triangle area = 1/2*base*height

1/2*c/a*c/b = 1/2c^2/ab

since a b c are in gp therefore c^2=ab

then

area= 1/2*ab/ab = area= 1/2

hence answer is B.

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