NIMCET 2017 — Mathematics PYQ

Concept:
The non zero number a, b, c are in H.P then $\frac{1}{a}$, $\frac{1}{b}$, $\frac{1}{c}$ are in AP
If a, b, c are in A.P then 2b = a + c

Calculations:
Given, The non zero number a, b, c are in H.P.
⇒ $\frac{1}{a}$, $\frac{1}{b}$, $\frac{1}{c}$ are in AP
Now,
⇒ $\frac{2}{b}=\frac{1}{a}+\frac{1}{c}$
⇒ $\frac{1}{a}+\frac{1}{c}-\frac{2}{b}=0$ ....(1)
Also, given $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ ....(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 $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ always passes through a fixed point, then the point is (1, -2)