If non zero numbers a, b, c are in H.P., then the straight line (x/a) + (y/b) + (1/c) = 0 always passes through a fixed point. That point is

Question

If non zero numbers a, b, c are in H.P., then the straight line (x/a) + (y/b) + (1/c) = 0 always passes through a fixed point. That point is (A) (- 1, 2) (B) (- 1, - 2) (C) (1, - 2) (D) (1, - (1/2))

Tardigrade Admin · Accepted Answer

a, b, c are in H.P. ⇒ (1/a), (1/b), (1/c) are in A.P. ⇒ (2/b) = (1/a) + (1/c) ⇒ (1/a) - (2/b) + (1/c) = 0 ∴ (x/a) + (y/b) + (1/c) = 0 passes through (1, -2)

Q. If non zero numbers a, b, c are in H.P., then the straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed point. That point is

(- 1, 2)

(- 1, - 2)

(1, - 2)

$(1, - \frac{1}{2})$

a, b, c are in H.P. $\Rightarrow \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in A.P.
$\Rightarrow \frac{2}{b} = \frac{1}{a} + \frac{1}{c} \Rightarrow \frac{1}{a} - \frac{2}{b} + \frac{1}{c} = 0$
$∴ \frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ passes through (1, -2)

Q. If non zero numbers a, b, c are in H.P., then the straight line ax​+by​+c1​=0 always passes through a fixed point. That point is