First slide

Cartesian plane

Question

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

Easy

A

(-1 /2)
B

(1, - 2)
C

(-1,-2)
D

(-1,2)

Solution

It is given that a, b, care in H.P
$\begin{array}{ll} ∴ \frac{2}{b} = \frac{1}{a} + \frac{1}{c} \\ \Rightarrow \frac{1}{a} + \frac{(- 2)}{b} + \frac{1}{c} = 0 \end{array}$
$\Rightarrow \frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ passes through the fixed point (1, - 2).

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