Question

if three non zero real numbers a,b,c are in harmonic progression then the straight lines x/a + y/b - 2/c =0 are concurrent at the point​

Answer 1

a,b,c are in H.P

∴

a

1

,

b

1

,

c

1

are in A.P

∴

b

2

=

a

1

+

c

1

________ (1)

∴

a

x

+

b

y

+

c

1

=0 ________ (2)

∴ From (1)

a

1

+

c

1

−

b

2

=0 ______ (3)

∴ From (2) & (3)

We infer that,

(x=1,y=−2)

∴ Point is (1,−2)