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  4. 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

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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

Three Dimensional Geometry

Solution:

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$
$ \therefore \frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0 $ passes through (1, -2)