UPSC NDA Math Model Paper 2

Given, The non zero number a, b, c are in H.P.

⇒

1

a

,

1

b

,

1

c

are in AP
Now,
⇒

2

b

=

1

a

+

1

c

⇒

1

a

+

1

c

−

2

b

=0 ........(1)
Also, given

x

a

+

y

b

+

1

c

=0 ..........(2)
From equation (1) and (2), we have
x=1,y=−2
Hence, if non zero number a, b, c are in A.P, then the straight line

x

a

+

y

b

+

1

c

=0 always passes through a fixed point, then the point is (1, - 2)